MODELING, ANALYSIS, IDENTIFICATION AND CONTROL OF MULTIVARIABLE SYSTEMS

Antonio Sala
Universitat Politècnica de València

Documents and audio/video compilation
 
05/08/2025 [13:30]
   Number of learning objects: 165
   Total video time: 42:08:16
[Own (165): 42:08:16; from third parties (0): 00:00:00]
[Link to PDF versión]
©2025, Antonio Sala Piqueras, DISA-UPV.
Subscribe to companion YouTube channels: [@asalacontrol, Español] [@ASalaControlEN, English]
I Presentation
1 Modelling and simulation
1.1 Basic Math review for newcomers
1.2 Introduction to modelling
1.3 Linearization
1.4 Simulation
1.4.1 Gravitational interaction of several bodies
1.4.2 Interactive simulation
1.5 Solving Ordinary Differential Equations
1.5.1 Matlab dsolve
1.5.2 Intuition on linear systems response
1.5.3 Laplace transform techniques for time response
1.6 Case studies
1.6.1 HVAC operating point thought experiment
1.6.2 DC motor plus gearbox
1.6.3 Tubular heater case study
1.6.4 Spring-mass case study
1.7 Phugoid mode of aircraft (longitudinal flight dynamics)
2 PID control
2.1 Intuitive trial-and-error approach
2.2 Double integrator (motion control) case study
3 Control structures
3.1 Manipulated and Controlled Variable selection, 2x3 process
3.2 Control with excess actuators (manipulated variables)
3.3 SVD decoupling
3.4 Case Study: mixer/heater process
3.5 SUMMARY: the BIG picture in day-to-day control in industry
4 Other isolated things for the moment being.
4.1 Linear matrix inequalities (LMI), Semidefinite programming (SDP)
4.1.1 LMI problems with ellipses
4.1.2 Geometry of generic LMI/SDP-representable sets
5 Robust Control
6 Manipulability and Force ellipsoids in Robotics
6.1 Manipulability ellipsoid: speed locus
6.2 Force ellipsoid
7 Statistics and data mining
7.1 Introduction to probability and recursive Bayes filter: ‘roaring tiger’ case study
7.2 Other statistics concepts
Classification (problem statement)
7.3 Stochastic processes (Gaussian processes)
7.3.1 Multi-output GP
7.3.2 Derivatives of a Gaussian process
7.3.3 The Matern kernel, intuition and limit cases
7.3.4 Stochastic processes in state-space form
7.4 Bayesian Optimization
7.4.1 Introduction and methodology outline
7.4.2 In-depth detail and examples

Chapter I
Presentation

This is a compilation of my materials in English and associated videos. You have many more in Spanish but, well, as there are many more choices in English (competition is fierce), I started recording videos in English quite late compared to Spanish. Sorry for the lack of content and disconnection between videos on the same topic, compared to the Spanish version.

Antonio Sala

Departamento de Ingeniería de Sistemas y Automática

Universitat Politècnica de València

Note on originality

These materials deal with content which is already “settled” in the scientific community, many of them already “classic”, developed twenty or more years ago. Most of the ideas and algorithms are thus well known to those skilled in these topics, and thus no ”research” originality is claimed thereon.

The only “originality” is in the “didactic” arena: the selection criteria and prioritization of the concepts, the organization of the materials and the way of presenting them in the transparencies and examples provided here. Therefore, this document or those linked to it should not be cited in a “research” context as an authoritative source for engineering recommendations or mathematical results/demonstrations, as they are not original/seminal. Expository considerations, thinking of the target audience (undergraduate/master students), intentionally make simplifications, variations, or assertions not entirely justified.

To avoid distracting the reader’s attention, the profusion of citations that is common in research texts has been avoided. However, it is explicitly stated here that there are abundant monographs that develop (in many cases, with much more depth and formalism) practically all of the concepts discussed here. Once familiar with the basic ideas, the student who wants more detail of the ideas in this text should consult his professor or TFM/Thesis supervisor, so that he can be referred to the corresponding authoritative references or seminal contributions.

Usage Rights

Regarding material under my authorship, all rights of use, copy, and intellectual property of the materials in this document and the audiovisual materials/PDF/linked code from it are reserved, both with respect to their verbatim usage or as a basis for derivative works. Nevertheless, use for personal study, by students and professors of public universities in official degrees, and the recommendation by their professors of this document is excepted from this reservation and expressly authorized. In another context (paid courses, academies, publications, commercial websites, …), do contact me if you intend to get money or merit from these or derivative works and let me in.

Chapter 1
Modelling and simulation

1.1 Basic Math review for newcomers

[1: derivsmlENJacobians, Partial and Total derivatives: Matlab example *** PIC 15:17 *Enlace a Spanish version

[2: maprENProjection Matrices: quick introduction *** PIC 15:13 *Enlace a Spanish version

Ellipsoids

[3: ellip1ENEllipsoids, positive definite matrices (1): basic definitions and motivation ** PIC 16:29 *Enlace a Spanish version

[4: ellip2ENEllipsoids (2): geometric interpretation of diagonalization, alternate representations of ellipsoids ** PIC 14:59 *Enlace a Spanish version

[5: ellip3ENEllipsoids (3): 3D examples, degenerate cases, hyperboloids ** PIC 08:28 *Enlace a Spanish version

[6: ellip4ENEllipsoids (4): equivalence of representations **** PIC 14:25 *Enlace a Spanish version

[7: ellip5ENEllipsoids (5): inclusion, inscribed/circunscribed sphere **** PIC 18:03 *Enlace a Spanish version

[8: ellip6ENEllipsoids (6): cuts/transformations/projections *** PIC 09:51 *Enlace a Spanish version

[9: ellip7ENEllipsoids (7): relationship with singular value decomposition (SVD) **** PIC 09:41

1.2 Introduction to modelling

[10: modelsintroENMathematical and computational (digital twin) models of physical systems: motivation, practical use ** PIC 15:57 *Enlace a Spanish version

[11: pinionmENPinion-rack dynamical model: Newton equations, equivalent mass/moment of inertia, reaction force ** PIC 15:31 *Enlace a Spanish version

[12: pinionELENPinion-rack dynamical model: Euler-Lagrange equations with kinematic constraints **** PIC 17:13

[13: tiovELEN2DoF dynamics of a carousel (rotational pendulum): Euler-Lagrange equations **** PIC 19:50

[14: tiovEL2EN2DoF dynamics of a carousel via Euler-Lagrange equations: particular cases *** PIC 13:15

1.3 Linearization

[15: linmiso1ENLinearization of function of 2 variables: Matlab example (symbolic toolbox), Taylor series revision ** PIC 16:57 *Enlace a Spanish version

[16: linmiso2ENLinearization of function of 2 variables, Matlab: linearization error analysis, Hessian eigenvalues *** PIC 09:04 *Enlace a Spanish version

1.4 Simulation

[17: tiovELsimEN2DoF dynamics of a carousel: simulation and animation *** PIC 12:43

[18: bcode45ENSimulation with ode45 of a closed-loop system (Matlab): inverted pendulum with PD controller *** PIC 18:14 *Enlace a Spanish version

[19: ode45vs15sENNumerical integration: comparison ode45 versus ode15s in stiff/ non-stiff ODEs (Matlab example) ** PIC 10:46 *Enlace a Spanish version

[20: aproxretENTransport Delay Approximation: simulation and comparison of options (PDE, Padé, finite element) *** PIC 17:38 *Enlace a Spanish version

1.4.1 Gravitational interaction of several bodies

[21: nbdsimcENN-body simulation of gravitational interaction: Matlab code/animation ode113 *** PIC 16:42 *Enlace a Spanish version

[22: nbdsim1ENN-body simulation of gravitational interaction examples: ellipses, chaos, escape velocity ** PIC 16:15

1.4.2 Interactive simulation

[23: interactankENInteractive simulation of a liquid tank: Matlab class, source code detail **** PIC 14:56 *Enlace a Spanish version

1.5 Solving Ordinary Differential Equations

1.5.1 Matlab dsolve

[24: masmusym1ENSolving ordinary differential equations (ODE) with Matlab (dsolve): mass-spring free response ** PIC 10:16 *Enlace a Spanish version

[25: masmusym2ENSolving ordinary differential equations (ODE) with Matlab (dsolve): mass-spring state-space form ** PIC 10:08 *Enlace a Spanish version

[26: masmuAnimENAnimating the time response of a mass-spring system: Matlab animation code and effect of damping *** PIC 12:35 *Enlace a Spanish version

[27: masmusymForzENSolving ordinary differential equations (ODE) with Matlab (dsolve): mass-spring forced response *** PIC 13:41 *Enlace a Spanish version

1.5.2 Intuition on linear systems response

[28: linregla3ENIntuition on linear dynamics: open loop control by sequence of steps (1st-order plant) * PIC 13:13 *Enlace a Spanish version

[29: linregla3ord2ENIntuition on linear dynamics: open loop control sequence of steps, 2nd order plant doesn’t work well *** PIC 10:12 *Enlace a Spanish version

1.5.3 Laplace transform techniques for time response

[30: RCRmodENModelling series RC circuit with leakage resistance: state space + Laplace domain (Symbolic toolbox) ** PIC 08:52

[31: sinpulLENLaplace transform of a sinusoidal pulse (semiperiod) ** PIC 11:56 *Enlace a Spanish version

[32: sinpulRCRENTime response of RCR circuit to single sinusoidal pulse (1: Laplace, superposition) ** PIC 11:49 *Enlace a Spanish version

[33: sinpulRCR2ENTime response of RCR circuit to single sinusoidal pulse (2: piecewise) *** PIC 10:59 *Enlace a Spanish version

[34: trenpulRCRENTime response of RCR circuit to a sinusoidal pulse train **** PIC 16:44 *Enlace a Spanish version

1.6 Case studies

1.6.1 HVAC operating point thought experiment

[35: hvacop1ENOperating point optimization: an air-conditioning (idealised) case study *** PIC 22:40 *Enlace a Spanish version

[36: hvacop2ENOptimal selection of operating point and controlled variables: air-conditioning thought experiment **** PIC 17:14 *Enlace a Spanish version

1.6.2 DC motor plus gearbox

In ellaboration.

1.6.3 Tubular heater case study

[37: termrdmapENTubular heater case study: ROADMAP * PIC 06:51

[38: term1eENModelling the dynamics of a heating tank (1st order, perfect mixing, incompressible flow) *** PIC 12:52 *Enlace a Spanish version

[39: termedpENPartial Differential Equation (PDE) modelling of a one-dimensional tubular heater for liquid fluids **** PIC 16:16 *Enlace a Spanish version

[40: termedpsolENPartial Differential Equations tubular heat exchanger: PDE solution via Laplace transform (transfer function) ***** PIC 19:57 *Enlace a Spanish version

[41: term1expENTransient modelling of tubular heat exchanger: 1st order, exponential temperature profile assumption **** PIC 22:42 *Enlace a Spanish version

[42: termedpstepENStep response (inlet temp, heating power) of the PDE solution of a tubular heater transient dynamics *** PIC 12:47 *Enlace a Spanish version

[43: term1evsedpENTubular heat exchanger: Comparison between exact EDP solution and 1st, 3rd order approximations **** PIC 17:56 *Enlace a Spanish version

[44: tubulFE1ENTubular heater/exchanger: finite element modelling (1) ***** PIC 15:06 *Enlace a Spanish version

[45: tubulFEsim1ENTubular heater/exchanger, finite elements: numerical simulation (1) **** PIC 13:59 *Enlace a Spanish version

[46: tubulFEsim2ENTubular heater/exchanger, finite elements: numerical simulation (2) **** PIC 12:25 *Enlace a Spanish version

[47: tubulconcENTubular heater/exchanger case study: recap and guidelines on model complexity choice *** PIC 16:31 *Enlace a Spanish version

1.6.4 Spring-mass case study

[48: moll3modENFirst-principle modelling of a 3 mass, 4 spring mechanical system (state-space internal representation) ** PIC 10:00 *Enlace a Spanish version

[49: moll3mod2ENFirst-principle modelling of a 3 mass, 4 spring mechanical system: recap and normalised matrix form ** PIC 14:00 *Enlace a Spanish version

[50: moll3sim1ENFirst-principle model of a 3 mass, 4 spring mechanical system: ode45 vs lsim simulation ** PIC 12:54 *Enlace a Spanish version

[51: moll3aniEN3 mass, 4 spring mechanical system: animation of free and forced response examples ** PIC 12:58 *Enlace a Spanish version

[52: moll3freeEN3 mass, 4 spring mechanical system: modal analysis of free response oscillations *** PIC 15:10 *Enlace a Spanish version

1.7 Phugoid mode of aircraft (longitudinal flight dynamics)

[53: intrid1ENDynamics of planar movement in intrinsic (Tangent, Normal) coordinates (2 DoF point mass) ** PIC 16:40 *Enlace a Spanish version

[54: fugoid1ENLongitudinal phugoid mode dynamics of an aircraft/glider (simplified 2nd order ODE) *** PIC 16:13 *Enlace a Spanish version

[55: fugsimENAircraft phugoid mode (simplified equations): discussion on simulation/animation examples *** PIC 12:38 *Enlace a Spanish version

[56: fugeqlinENPhugoid aircraft dynamics: equilibrium, linearization, stability (simplified 2nd order equations) *** PIC 17:59 *Enlace a Spanish version

[57: fugsimcodENAircraft phugoid glide (simplified equations): ode45 simulation and animation code (Matlab) *** PIC 12:53 *Enlace a Spanish version

Chapter 2
PID control

In preparation, I’m recording/editing a subset of the videos I have in my Spanish channel.

2.1 Intuitive trial-and-error approach

[58: dintpid1motENDouble-integrator and its control (1): motivation ** PIC 17:54

[59: dintpid2tunENDouble integrator and its control: trial and error controller tuning [1: PD] *** PIC 18:37

[60: dintpid2tunBENDouble integrator and its control: trial and error PID tuning [2, PID; 3., advanced tweaks] *** PIC 11:25

2.2 Double integrator (motion control) case study

[61: dintteostENDouble integrator, PD control: stability *** PIC 20:59

[62: dintteoerrENDouble integrator, PD control: position and velocity errors (setpoint tracking and disturbance rejection) *** PIC 13:51

[63: dintPDplaceENdouble-integrator PD design via pole placement *** PIC 23:38

[64: dintPIDplaceENdouble-integrator PID design via pole placement *** PIC 21:49

Chapter 3
Control structures

3.1 Manipulated and Controlled Variable selection, 2x3 process

[65: sacerf1ENControlled/manipulated variable selection: setpoint tracking, SVD, Matlab example (1) *** PIC 14:43 *Enlace a Spanish version

[66: sacerf2ENControlled/manipulated variable selection: setpoint tracking, full SVD, reachable ellipsoid, Matlab (2) **** PIC 14:09 *Enlace a Spanish version

[67: sacerf3ENControlled/manipulated variable selection: setpoint tracking, polyhedra (linprog) Matlab example (3) **** PIC 18:40 *Enlace a Spanish version

[68: sacerf4ENControlled/manipulated variable selection: total disturbance rejection Matlab example (4) **** PIC 17:55 *Enlace a Spanish version

[69: sacerf5ENControlled/manipulated variable selection: partial disturbance rejection, polyhedra quadprog (5) **** PIC 13:46 *Enlace a Spanish version

[70: sacerf6ENControlled/manipulated variable selection: partial disturbance rejection, SVD (6) **** PIC 16:51 *Enlace a Spanish version

[71: sacerf7ENControlled/manipulated variable selection: transient analysis, sigma plot (7) *** PIC 14:55 *Enlace a Spanish version

3.2 Control with excess actuators (manipulated variables)

[72: dosact1ENControl with excess actuators (1): load balancing, split range, override *** PIC 18:58 *Enlace a Spanish version

[73: dosact2ENControl with excess actuators (2): cascade extra actuator, gradual, double cascade **** PIC 19:40 *Enlace a Spanish version

3.3 SVD decoupling

[74: dsvdintu1ENSVD decoupling and principal maneuvers in process control (1): theory outline *** PIC 17:40 *Enlace a Spanish version

[75: dsvdintu2ENSVD decoupling case study (2): one controlled variable, two manipulated variables *** PIC 17:09 *Enlace a Spanish version

3.4 Case Study: mixer/heater process

[76: estrx2aENTwo tank mixing + heating system (1): basic multiloop control, case study *** PIC 12:45 *Enlace a Spanish version

[77: estrx2bENTwo tank mixing + heating system (2): advanced cascade feedforward ratio control case study **** PIC 21:45 *Enlace a Spanish version

[78: mzrgaENstatic mixing + flow control: multiloop control via relative gain array (RGA), theory *** PIC 12:02 *Enlace a Spanish version

[79: mzratdc1ENstatic mixing + flow control: ratio control, linearization and relation to mutiloop/decoupling ***** PIC 14:13 *Enlace a Spanish version

[80: mzratdc2ENstatic mixing + flow control: decoupling in direct/inverted form, linear and nonlinear ***** PIC 18:54 *Enlace a Spanish version

3.5 SUMMARY: the BIG picture in day-to-day control in industry

Chapter 4
Other isolated things for the moment being.

[81: imcQcteENIMC control of a fast process: constant Q *** PIC 09:21 *Enlace a Spanish version

[82: fblin1ENFeedback linearization and decoupling: two-input two-output example (hand-made, no Matlab) **** PIC 14:36 *Enlace a Spanish version

4.1 Linear matrix inequalities (LMI), Semidefinite programming (SDP)

4.1.1 LMI problems with ellipses

[83: lmielout1ENLMIs: Ellipsoid containing other ellipsoids/polyhedra, Yalmip/Sedumi/Matlab (1): minimum major axis **** PIC 18:43

[84: lmielout2ENLMIs: Ellipsoid containing other ellipsoids/polyhedra, Yalmip/Sedumi/Matlab (2): minimum area **** PIC 09:39

[85: lmielin1ENLMI demos: largest ellipse inside other poliedra/ellipses (1) **** PIC 16:49

[86: lmielin2ENLMI demos: largest ellipse inside other poliedra/ellipses (2), largest area (geomean) ***** PIC 16:18

[87: distelliENDistance between ellipses: semidefinite programming (SDP/LMI, linear matrix inequalities) **** PIC 10:59

[88: elinncENMaximum volume ellipsoid inside polyhedron and other ellipsoids: 2D example, Matlab (LMI/SDP) ***** PIC 15:36

4.1.2 Geometry of generic LMI/SDP-representable sets

[89: lmisets1ENLMI sets (SDP-representable sets, spectrahedra): definition, basic properties and 2D examples **** PIC 17:42

[90: lmisets2ENLifted LMI sets, 2D examples (Matlab, YALMIP) **** PIC 13:56

[91: lmisets3ENLMI sets (3): plotting routine and applications **** PIC 09:54

[92: lmisets4ENLMI sets (4): scaling, perspective cones, set interpolation, convex hull ***** PIC 20:15

Chapter 5
Robust Control

[93: prth1ENRobust performance: small-gain sufficient condition (h-infinity norm bound) **** PIC 10:59

[94: stabmrgENRobust stability margins: robstab, wcgain, robgain example 2nd order system with uncertain damping **** PIC 12:56 *Enlace a Spanish version

[95: cerp1ENRobust performance case study (Matlab) 1: problem statement and simulation-based robustness validation *** PIC 15:32 *Enlace a Spanish version

[96: cerp2ENRobust performance case study (Matlab) 2: generalised plant, norm-based performance PID certification **** PIC 16:20 *Enlace a Spanish version

[97: cerp3ENRobust performance case study (Matlab) 3: scaled small gain and h-infinity optimization (approx. musyn) ***** PIC 13:31 *Enlace a Spanish version

[98: cerp4muENRobust performance case study (Matlab) 4: mu-synthesis (building uncertain generalised plants) ***** PIC 11:27 *Enlace a Spanish version

[99: cerp5muENRobust performance case study (Matlab) 5: mu-synthesis order reduction, PID tuning, loop simulations **** PIC 16:15 *Enlace a Spanish version

[100: gapm1ENNormalised factorisation uncertainty: nu-gap metric and its geometric interpretation (simplified, real, SISO) -1- **** PIC 10:50 *Enlace a Spanish version

[101: gapm1bENNormalised coprime factorisation uncertainty: nu-gap metric and its geometric interpretation (simplified, real, SISO) -2- **** PIC 14:16

[102: gapm2ENNormalised factorisation uncertainty: nu-gap metric geometric interpretation, general case (no proofs) **** PIC 11:35 *Enlace a Spanish version

[103: obsmu1ENLFT modelling of a system with uncertain damping for force estimation **** PIC 13:26 *Enlace a Spanish version

[104: obsmu2ENForce estimation in an uncertain mechanical system: h2, hinf, musyn Matlab example ***** PIC 19:55 *Enlace a Spanish version

[105: obsmu3ENForce estimation in uncertain mechanical system: h2-hinf-musyn performance analysis, frequency domain **** PIC 13:53 *Enlace a Spanish version

[106: obsmu4ENForce estimation in uncertain mechanical system: h2-hinf-musyn performance analysis, time domain ***** PIC 19:20 *Enlace a Spanish version

Chapter 6
Manipulability and Force ellipsoids in Robotics

6.1 Manipulability ellipsoid: speed locus

[107: elipm1ENManipulability of robotic arm (1): modelling, jacobian, singular value decomposition *** PIC 16:33

[108: elipm2ENManipulabilifty ellipsoid of robot arm (2): theory, example, polyhedron approach **** PIC 17:52

[109: elipm3ENManipulabilifty ellipsoid of robot (3): further examples and animations *** PIC 12:23

6.2 Force ellipsoid

[110: elipf1ENJacobian: matrix gear ratio, effect on force/torque multiplication **** PIC 20:22

[111: elipf2ENForce ellipsoid in a robot (1): definition and basic examples *** PIC 11:53

[112: elipf3ENForce ellipsoid in a robot (2): principal maneuvers, Jacobian singular value decomposition **** PIC 14:41

[113: elipf4ENDuality of force/manipulability ellipsoids in a robot (inverse behaviour) *** PIC 14:43

Chapter 7
Statistics and data mining

7.1 Introduction to probability and recursive Bayes filter: ‘roaring tiger’ case study

This case study will present a simple-to-understand ‘zookeeper’ task that will motivate and introduce a series of basic concepts in probability and statistics and end with a recursive Bayes filter (almost!, state transitions are not present).

[114: tiger1ENHidden tiger (1): Conditional, prior and joint probability tables; problem description * PIC 22:26 *Enlace a Spanish version

[115: tiger2ENHidden tiger (2): from joint to marginal and conditional; direct/inverse conditional tables * PIC 20:34 *Enlace a Spanish version

[116: tiger3ENHidden tiger (3): marginal, conditional, Bayes rule, graphical interpretation ** PIC 21:20 *Enlace a Spanish version

[117: tiger4ENHidden tiger (4): conditional and Bayes rule for TWO roars ** PIC 13:44 *Enlace a Spanish version

[118: tiger5ENHidden tiger (5): Bayes formula for any number of roars (non-recursive) *** PIC 16:18 *Enlace a Spanish version

[119: tiger6brENHidden tiger (6): recursive Bayes formula for any number of roars (proof) **** PIC 15:55 *Enlace a Spanish version

[120: tiger7rbsENHidden tiger (7): recursive Bayes formula (simulation, Matlab) *** PIC 17:40 *Enlace a Spanish version

7.2 Other statistics concepts

[121: cfrc1EN2D Gaussian distribution: confidence rectangles and ellipses (Matlab example) ** PIC 18:51 *Enlace a Spanish version

[122: cfrcwrongEN2D Gaussian distribution: remark on confidence rectangles and ellipses with correlated variables (Matlab example) *** PIC 08:29 *Enlace a Spanish version

[123: condin1ENConditional independence (I): definitions and basic examples *** PIC 18:42 *Enlace a Spanish version

[124: condin2ENConditional Independence (II): control-relevant examples (Markov hypothesis), Bayesian Networks *** PIC 15:27 *Enlace a Spanish version

[125: vcinv1ENBest linear prediction: from covariance to linear model with additive noise and vice-versa (theory) *** PIC 09:20 *Enlace a Spanish version

[126: vcinv1bENBest linear prediction, inverse models in statistical sense: example (I) *** PIC 15:46

[127: vcinv2ENBest linear prediction, inverse models in statistical sense: example (II) *** PIC 10:10 *Enlace a Spanish version

[128: condnocoENConditional Independence (III): conditionally UNcorrelated random variables (only multivariate normal distribution) **** PIC 17:13 *Enlace a Spanish version

[129: pcaissvdENComparing PCA (statistics toolbox) with SVD (built-in, Matlab): identical results ** PIC 03:59 *Enlace a Spanish version

[130: tls51ENTotal Least Squares with 5 variables: Matlab example *** PIC 18:30 *Enlace a Spanish version

[131: tls52ENTotal Least Squares with 5 variables: Matlab example 2, wrong scaling **** PIC 11:10 *Enlace a Spanish version

Classification (problem statement) [132: clasifintr1ENModel fitting for classification (1): problem statement (deterministic version) * PIC 16:28 *Enlace a Spanish version

[133: clasifintr2ENModel fitting for classification (2): probabilistic version of problem statement ** PIC 15:41 *Enlace a Spanish version

[134: clasifNoLSENModel fitting for classification (3): are Least Squares a sensible choice? *** PIC 16:51 *Enlace a Spanish version

7.3 Stochastic processes (Gaussian processes)

[135: estoc1ENStochastic processes (random functions) in engineering: motivation, definitions, examples ** PIC 15:40 *Enlace a Spanish version

[136: gpsambENSampling a Gaussian process (realizations), Matlab example *** PIC 13:57 *Enlace a Spanish version

[137: gpsambpoENSampling a Gaussian process with some observations (sampling the posterior), Matlab example **** PIC 14:55 *Enlace a Spanish version

[138: gpkh2ENKarhunen-Loeve (PCA) components of a Gaussian Process: Matlab example (1) **** PIC 18:47 *Enlace a Spanish version

[139: gpkh2pENKarhunen-Loeve (PCA) components of a Gaussian Process: Matlab example (2), animation and posterior **** PIC 16:44 *Enlace a Spanish version

[140: gpcholENGaussian process: Cholesky factor of covariance, spectral factor (Matlab example) ***** PIC 19:34

[141: gpanticaENGaussian process: anticausal and bilateral representations (Matlab example) ***** PIC 13:48

7.3.1 Multi-output GP

[142: mimoGP1EN(1/5) Multi-Output Gaussian Processes: Motivation *** PIC 15:34

[143: mimogp2EN(2/5) Multi-Output Gaussian Processes: representation; code for realizations **** PIC 21:58

[144: mimogp3pcaEN(3/5) Multi-output Gaussian Processes: principal component analysis, Karhunen-Loeve eigenfunctions **** PIC 09:46

[145: mimogp4predAEN(4/5) Multi-output Gaussian Processes: joint prediction **** PIC 17:42

[146: mimogp5predUEN(5/5) Multi-output Gaussian Processes: latent factor estimation **** PIC 22:55

7.3.2 Derivatives of a Gaussian process

[147: gradgpENMean and covariance of the partial derivatives (gradient, velocity) of a stochastic process ***** PIC 17:54 *Enlace a Spanish version

[148: gradgpstENDerivatives of a stochastic process via Jacobian/Hessian of covariance: stationary case ***** PIC 13:54 *Enlace a Spanish version

[149: gpvel1ENGaussian Processes: covariance between position and speed example (1) **** PIC 14:27 *Enlace a Spanish version

[150: gpvel2ENGaussian Processes: covariance between position and speed example (2), prediction **** PIC 19:57 *Enlace a Spanish version

7.3.3 The Matern kernel, intuition and limit cases

[151: maternENMatérn kernel and squared-exponential one: intuition as a filter with repeated real poles **** PIC 14:35

[152: maternr1ENMatérn kernel regression (1): basic setup, 1st order filter example, linear interpolation *** PIC 16:40

[153: maternr2ENMatérn kernel regression (2): 2nd 3rd and fractional order, splines, Gaussian filter examples ***** PIC 17:25

7.3.4 Stochastic processes in state-space form

[154: ekfteoENExtended Kalman filter for nonlinear state estimation (theory) **** PIC 17:28 *Enlace a Spanish version

[155: vanloanENVan Loan’s expm formula for variance discretization in linear stochastic ODEs **** PIC 15:58 *Enlace a Spanish version

7.4 Bayesian Optimization

7.4.1 Introduction and methodology outline

[156: BOmot1ENBayesian Optimization motivation (1/4): problem statement and model classes ** PIC 15:40 *Enlace a Spanish version

[157: BOmot2ENBayesian Optimization motivation (2/4): methodology outline *** PIC 11:20 *Enlace a Spanish version

[158: BOmot3ENBayesian Optimization motivation (3/4): computation of posterior and decision (acquisition) on next sample (outline) **** PIC 10:49 *Enlace a Spanish version

[159: BOmot4ENBayesian Optimization motivation (4/4): recommended application domains, remarks ** PIC 19:33 *Enlace a Spanish version

[160: boloop1ENBayesian Optimization loop: a quick example of the methodology *** PIC 12:29

7.4.2 In-depth detail and examples

[161: boinopENBayesian optimization: implicit information about the optimum in a Gaussian process *** PIC 18:53

[162: boPIENBayesian Optimization: probability of improvement, example **** PIC 20:45

[163: boEIENBayesian Optimization: expected improvement, example (+LCB,PI,EV) **** PIC 19:58

[164: boloop2ENBayesian optimization: PI, EI, LCB detailed example (Matlab) **** PIC 15:59

[165: boloop3ENBayesian optimization: bad performance examples ***** PIC 17:17