




Courses

Robust Control(SPRING_2017)
Aims:
In this course the concept of structured and unstructured model uncertainties in system model are introduced and stability and performance analysis of feedback system in the presence of model uncertainty is discussed. Also, robust synthesis methods of H? controllers and ?analysis for uncertain systems are introduced
Syllabus:
 Overview of robust control
 Introduction on linear algebra & linear dynamical systems
 Linear spaces, Innerproduct spaces, Hilbert spaces, Banach spaces, H_2 and H_infinity spaces, norms of signals and systems, Relation between signals and systems norm, Computing H_2 and H_infinity norms, Frequencydomain interpretation of H_infinity norm, Timedomain interpretation of H_infinity norm
 Internal stability, Wellposedness, Coprime Factorization, Plant factorization, Coprime Factorization of a stabilizing controller
 Performance Specifications, Feedback properties, performance tradeoffs & design limitations, sensitivity transfer matrices, Weighted H_2 & H_? problems, H_2& H_? mixedsensitivity, analyticity or interpolation conditions, waterbed effect.
 Modeling uncertainty and robustness, representation of uncertainties, structured and unstructured uncertainties, parameterized, additive and multiplicative uncertainties, Robust Stability, Robust Performance, Smallgain Theorem , Robustness for Unstructured Uncertainties
 Linear Fractional Transformation (LFT), Formulation of control problems in LFT framework, parameterization of all stabilizing controller,
 mu synthesis, structured singular value, structured robust stability, robust performance
 Algebraic Riccati Equations (AREs), stabilizing solutions for ARE, Bounded Real Lemma (BRL)
 H_infinity control problem
 Introduction to convex optimization, introduction to Linear Matrix Inequalities (LMIs), application of LMIs in H_2 & H_infinity optimal control problems
 کاهش مدل ( تحقق متوازن، روش برش متوازن، کاهش مرتبه کنترل کننده)
Text Book:
 K. Zhou and J. Doyle, "Essentials of robust control", Prentice Hall, 1998

Advanced Topics in Multi Agent Systems(FALL_2016)
Aims:
In this course, analysis and synthesis methods are discussed for distributed controller design in multiagent systems. Also, the effect of switching interaction topologies, timedelays and measurement noises are investigated in such systems
Syllabus:
 Introduction to multiagent systems: Definitions, Motivations, Characteristics, Applications, Distributed control categorization, Emergent issues
 Introduction to algebraic graph theory: Preliminaries, Graph Laplacian, Eigenstructure of graph Laplacian, nonnegative matrices, ergodic (SIA) matrices, scrambling matrices, Mmatrix
 Distributed consensus protocols: Firstorder consensus protocols (Fixed topology/Switching topology, Continuoustime/Discretetime), Leaderfollowing case (Constant reference state, Timevarying reference state), Secondorder consensus protocols (Fixed topology/Switching topology, Bounded control input, No state derivative measurements, With group reference velocity/Partial access to a group reference state, Secondorder consensus with sampled data
 Containment control: Definitions, Applications, Multiple Stationary Leaders (Directed Fixed Interaction, Directed Switching Interaction), Multiple Dynamic Leaders (Directed Fixed Interaction, Directed Switching Interaction)
 Flocking algorithms:Flocking algorithm without group objective, Leaderfollowing flocking algorithm,Flocking algorithm with obstacle avoidance, Flocking with a minority of informed agents, Connectivitypreserving flocking algorithm, Connectivitypreserving flocking algorithm with bounded potential function, Adaptive flocking algorithms with nonlinear dynamics
 Timedelay in multiagent systems:Basic definitions, Types of timedelays in multiagent systems, Analysis techniques (Frequencydomain techniques, Techniques based on Lyapunovkrasovaskii function (LMI tool), Techniques based on Stochastic matrix theory), synthesis and analysis of delayed consensus protocols in switching networks (with timevarying delays)
 Stochastic setting:An overview on random variables, Stochastic version of LaSalle’s Theorem, Consensus definitions in stochastic setting, Consensus over random graph (Undirected edges with the same probability and the same weight, Directed edges with the different probabilities and different positive weights, Nonexpansive and pseudocontractive matrices, Directed edges with the different probabilities and different arbitrary weights)
 Measurement and communication noise:An overview on stochastic processes, Gaussian or normal process, Stationary Process, The concept of white noise, Process with independent increments, The Wiener process, Stochastic differential equations, Itô Rules, continuoustime mean square averageconsensus (with measurement noises, with measurement noises and timevarying communication timedelays, with measurement noises and arbitrary switching topology
Text Book:
 1 Distributed Coordination of Multiagent Networks: Emergent problems, Models and Issues, by Wei Ren, Yongcan Cao, Communications and Control Engineering Series, SpringerVerlag, London, 2011.
 2 Distributed Consensus in MultiVehicle Cooperative Control: Theory and Applications, by Wei Ren and Randal W. Beard, Communications and Control Engineering Series, SpringerVerlag, London, 2008.

Robust Control(SPRING_2016)
Aims:
In this course the concept of structured and unstructured model uncertainties in system model are introduced and stability and performance analysis of feedback system in the presence of model uncertainty is discussed. Also, robust synthesis methods of H? controllers and ?analysis for uncertain systems are introduced
Syllabus:
 Overview of robust control
 Introduction on linear algebra & linear dynamical systems
 Linear spaces, Innerproduct spaces, Hilbert spaces, Banach spaces, H_2 and H_infinity spaces, norms of signals and systems, Relation between signals and systems norm, Computing H_2 and H_infinity norms, Frequencydomain interpretation of H_infinity norm, Timedomain interpretation of H_infinity norm
 Internal stability, Wellposedness, Coprime Factorization, Plant factorization, Coprime Factorization of a stabilizing controller
 Performance Specifications, Feedback properties, performance tradeoffs & design limitations, sensitivity transfer matrices, Weighted H_2 & H_? problems, H_2& H_? mixedsensitivity, analyticity or interpolation conditions, waterbed effect.
 Modeling uncertainty and robustness, representation of uncertainties, structured and unstructured uncertainties, parameterized, additive and multiplicative uncertainties, Robust Stability, Robust Performance, Smallgain Theorem , Robustness for Unstructured Uncertainties
 Linear Fractional Transformation (LFT), Formulation of control problems in LFT framework, parameterization of all stabilizing controller,
 mu synthesis, structured singular value, structured robust stability, robust performance
 Algebraic Riccati Equations (AREs), stabilizing solutions for ARE, Bounded Real Lemma (BRL)
 H_infinity control problem
 Introduction to convex optimization, introduction to Linear Matrix Inequalities (LMIs), application of LMIs in H_2 & H_infinity optimal control problems
Text Book:
 K. Zhou and J. Doyle, "Essentials of robust control", Prentice Hall, 1998

Advanced Topics in Multi Agent Systems(FALL_2015)
Aims:
In this course, analysis and synthesis methods are discussed for distributed controller design in multiagent systems. Also, the effect of switching interaction topologies, timedelays and measurement noises are investigated in such systems
Syllabus:
 Introduction to multiagent systems: Definitions, Motivations, Characteristics, Applications, Distributed control categorization, Emergent issues
 Introduction to algebraic graph theory: Preliminaries, Graph Laplacian, Eigenstructure of graph Laplacian, nonnegative matrices, ergodic (SIA) matrices, scrambling matrices, Mmatrix
 Distributed consensus protocols: Firstorder consensus protocols (Fixed topology/Switching topology, Continuoustime/Discretetime), Leaderfollowing case (Constant reference state, Timevarying reference state), Secondorder consensus protocols (Fixed topology/Switching topology, Bounded control input, No state derivative measurements, With group reference velocity/Partial access to a group reference state, Secondorder consensus with sampled data
 Containment control: Definitions, Applications, Multiple Stationary Leaders (Directed Fixed Interaction, Directed Switching Interaction), Multiple Dynamic Leaders (Directed Fixed Interaction, Directed Switching Interaction)
 Flocking algorithms:Flocking algorithm without group objective, Leaderfollowing flocking algorithm,Flocking algorithm with obstacle avoidance, Flocking with a minority of informed agents, Connectivitypreserving flocking algorithm, Connectivitypreserving flocking algorithm with bounded potential function, Adaptive flocking algorithms with nonlinear dynamics
 Timedelay in multiagent systems:Basic definitions, Types of timedelays in multiagent systems, Analysis techniques (Frequencydomain techniques, Techniques based on Lyapunovkrasovaskii function (LMI tool), Techniques based on Stochastic matrix theory), synthesis and analysis of delayed consensus protocols in switching networks (with timevarying delays)
 Stochastic setting:An overview on random variables, Stochastic version of LaSalle’s Theorem, Consensus definitions in stochastic setting, Consensus over random graph (Undirected edges with the same probability and the same weight, Directed edges with the different probabilities and different positive weights, Nonexpansive and pseudocontractive matrices, Directed edges with the different probabilities and different arbitrary weights)
 Measurement and communication noise:An overview on stochastic processes, Gaussian or normal process, Stationary Process, The concept of white noise, Process with independent increments, The Wiener process, Stochastic differential equations, Itô Rules, continuoustime mean square averageconsensus (with measurement noises, with measurement noises and timevarying communication timedelays, with measurement noises and arbitrary switching topology
Text Book:
 1 Distributed Coordination of Multiagent Networks: Emergent problems, Models and Issues, by Wei Ren, Yongcan Cao, Communications and Control Engineering Series, SpringerVerlag, London, 2011.
 2 Distributed Consensus in MultiVehicle Cooperative Control: Theory and Applications, by Wei Ren and Randal W. Beard, Communications and Control Engineering Series, SpringerVerlag, London, 2008.

Linear Algebra(Introduction to Matrices (matrix addition and multiplication, matrix derivative and integral, matrix transpose, trace, identity matrix, block matrix , matrix polynomial, determinant, minor and cofactor, singular matrices, adjoint matrix, inverse matrix * •)
Aims:
This course covers matrix theory and linear algebra, emphasizing topics useful in many disciplines especially electrical engineering such as matrix algebra, determinants, norms and orthogonality, systems of linear equations, vector spaces and subspaces, linear transformations, eigenvalues and eigenvectors, similarity transformations, positive definite matrices, Jordanform and singular value decomposition. Also the application of linear algebra in state space analysis of LTI systems is introduce
Syllabus:
Text Book:
Introduction to vectors (vector addition, scalar multiplication, linear combination of vectors, inner product, vector norm, distance, angle, orthogonality)  •

Linear Algebra(Introduction to Matrices (matrix addition and multiplication, matrix derivative and integral, matrix transpose, trace, identity matrix, block matrix , matrix polynomial, determinant, minor and cofactor, singular matrices, adjoint matrix, inverse matrix * •)
Aims:
This course covers matrix theory and linear algebra, emphasizing topics useful in many disciplines especially electrical engineering such as matrix algebra, determinants, norms and orthogonality, systems of linear equations, vector spaces and subspaces, linear transformations, eigenvalues and eigenvectors, similarity transformations, positive definite matrices, Jordanform and singular value decomposition. Also the application of linear algebra in state space analysis of LTI systems is introduce
Syllabus:
Text Book:
Introduction to vectors (vector addition, scalar multiplication, linear combination of vectors, inner product, vector norm, distance, angle, orthogonality)  •

Modern Control(* CT Chen, Linear System Theory and Design, 3rd edition, Oxford Universiy Press, 1999 * علي خاكي صديق، اصول كنترل مدرن، انتشارات دانشگاه تهران، 1383)
Aims:
In this course, modelling and designing the control systems are investigated in the state space
Syllabus:
Text Book:
1Introduction to modern control systems: Control system definition, Control system physical components, Control system conceptual components, Controller designing procedure, Advantages of state space representation over transfer function representation  2 Introduction to linear algebra and matrix analysis: Vector space, Linear combination, Change of basis and coordinates in Ndimensional space, Linear transformation, Determinant, Eigenvalues and eigenvectors, Jordan canonical form, Matrix functions
 Linear systems representation: State space representation, system modelling based on physical principles, system modelling based on Lagrangian method, Linearization of Nonlinear differential equations, inputoutput representation of linear systems (transfer function, transmission zeros, transfer function poles), Linear system properties, Timedomain solution of LTI state equations
 computing methods for state transition matrix (Laplace method, CaleyHamilton method, Silvester method, Jordan form method), Similarity transformation, diagonal form, Blockdiagonal form, System dynamic modes, Modal decomposition, solution of LTI system to exponential input
 4 Controllability and observability: necessary and sufficient conditions for controllability, necessary and sufficient conditions for observability, Canonical Jordan form test method, Unstable polezero cancellation, Uncontrollable and unobservable systems decomposition, Kalman decomposition
 5 Realization theory : Minimal Realization (definitions and conditions), Realization of SISO systems (Controllable canonical form, Observable canonical form, Jordan canonical realization, Parallel and serial realization), Realization of MIMO systems, Realization of MISO systems, Realization of SIMO systems
 6 Stability: Definitions (Lyapunov stability, Asymptotically stability, Global asymptotically stability, BIBO stability, Internal stability), stability in LTI systems, stability of Nonlinear systems ( linearization method, Lyapunov method)
 7 Linear Timevarying (LTV) systems: Fundamental matrix, State transition matrix, solution of LTV system, Equivalent LTV equations, Timevarying realization, internal stability for LTV systems
 8 State feedback: state feedback controller design in SISO systems, state feedback gain (Bass and Gura method, Ackerman method, Controllable canonical realization method, state feedback effect on controllability and observability, state feedback effect on system zeros, state feedback for uncontrollable systems, state feedback design for multivariable systems
 9 State estimator (State observer): fullorder observer, Reducedorder observer, State feedback based controller with fullorder observer, Separation property, Regulation and tracking, Tracking with disturbance rejection, State feedback based controller with reducedorder observer
 10 Introduction to optimal control systems: Formulation of optimal control problem, LQR optimal feedback gain computation "

Modern Control(* CT Chen, Linear System Theory and Design, 3rd edition, Oxford Universiy Press, 1999 * علي خاكي صديق، اصول كنترل مدرن، انتشارات دانشگاه تهران، 1383)
Aims:
In this course, modelling and designing the control systems are investigated in state space
Syllabus:
Text Book:
Introduction to modern control systems: Control system definition, Control system physical components, Control system conceptual components, Controller designing procedure, Advantages of state space representation over transfer function representation  Introduction to linear algebra and matrix analysis: Vector space, Linear combination, Change of basis and coordinates in Ndimensional space, Linear transformation, Determinant, Eigenvalues and eigenvectors, Jordan canonical form, Matrix functions
 Linear systems representation: State space representation, system modelling based on physical principles, system modelling based on Lagrangian method, Linearization of Nonlinear differential equations, inputoutput representation of linear systems (transfer function, transmission zeros, transfer function poles), Linear system properties, Timedomain solution of LTI state equations
 computing methods for state transition matrix (Laplace method, CaleyHamilton method, Silvester method, Jordan form method), Similarity transformation, diagonal form, Blockdiagonal form, System dynamic modes, Modal decomposition, solution of LTI system to exponential input
 Controllability and observability: necessary and sufficient conditions for controllability, necessary and sufficient conditions for observability, Canonical Jordan form test method, Unstable polezero cancellation, Uncontrollable and unobservable systems decomposition, Kalman decomposition
 Realization theory : Minimal Realization (definitions and conditions), Realization of SISO systems (Controllable canonical form, Observable canonical form, Jordan canonical realization, Parallel and serial realization), Realization of MIMO systems, Realization of MISO systems, Realization of SIMO systems
 Stability: Definitions (Lyapunov stability, Asymptotically stability, Global asymptotically stability, BIBO stability, Internal stability), stability in LTI systems, stability of Nonlinear systems ( linearization method, Lyapunov method)
 Linear Timevarying (LTV) systems: Fundamental matrix, State transition matrix, solution of LTV system, Equivalent LTV equations, Timevarying realization, internal stability for LTV systems
 State feedback: state feedback controller design in SISO systems, state feedback gain (Bass and Gura method, Ackerman method, Controllable canonical realization method, state feedback effect on controllability and observability, state feedback effect on system zeros, state feedback for uncontrollable systems, state feedback design for multivariable systems
 State estimator (State observer): fullorder observer, Reducedorder observer, State feedback based controller with fullorder observer, Separation property, Regulation and tracking, Tracking with disturbance rejection, State feedback based controller with reducedorder observer "












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