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  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, Inner-product 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, Frequency-domain interpretation of H_infinity norm, Time-domain interpretation of H_infinity norm
  • Internal stability, Well-posedness, 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_? mixed-sensitivity, 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, Small-gain 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 multi-agent systems. Also, the effect of switching interaction topologies, time-delays and measurement noises are investigated in such systems

Syllabus:

  • Introduction to multi-agent 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, M-matrix
  • Distributed consensus protocols: First-order consensus protocols (Fixed topology/Switching topology, Continuous-time/Discrete-time), Leader-following case (Constant reference state, Time-varying reference state), Second-order consensus protocols (Fixed topology/Switching topology, Bounded control input, No state derivative measurements, With group reference velocity/Partial access to a group reference state, Second-order 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, Leader-following flocking algorithm,Flocking algorithm with obstacle avoidance, Flocking with a minority of informed agents, Connectivity-preserving flocking algorithm, Connectivity-preserving flocking algorithm with bounded potential function, Adaptive flocking algorithms with nonlinear dynamics
  • Time-delay in multi-agent systems:Basic definitions, Types of time-delays in multi-agent systems, Analysis techniques (Frequency-domain techniques, Techniques based on Lyapunov-krasovaskii function (LMI tool), Techniques based on Stochastic matrix theory), synthesis and analysis of delayed consensus protocols in switching networks (with time-varying 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, continuous-time mean square average-consensus (with measurement noises, with measurement noises and time-varying communication time-delays, with measurement noises and arbitrary switching topology

Text Book:

  • 1- Distributed Coordination of Multi-agent Networks: Emergent problems, Models and Issues, by Wei Ren, Yongcan Cao, Communications and Control Engineering Series, Springer-Verlag, London, 2011.
  • 2- Distributed Consensus in Multi-Vehicle Cooperative Control: Theory and Applications, by Wei Ren and Randal W. Beard, Communications and Control Engineering Series, Springer-Verlag, 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, Inner-product 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, Frequency-domain interpretation of H_infinity norm, Time-domain interpretation of H_infinity norm
  • Internal stability, Well-posedness, 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_? mixed-sensitivity, 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, Small-gain 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 multi-agent systems. Also, the effect of switching interaction topologies, time-delays and measurement noises are investigated in such systems

Syllabus:

  • Introduction to multi-agent 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, M-matrix
  • Distributed consensus protocols: First-order consensus protocols (Fixed topology/Switching topology, Continuous-time/Discrete-time), Leader-following case (Constant reference state, Time-varying reference state), Second-order consensus protocols (Fixed topology/Switching topology, Bounded control input, No state derivative measurements, With group reference velocity/Partial access to a group reference state, Second-order 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, Leader-following flocking algorithm,Flocking algorithm with obstacle avoidance, Flocking with a minority of informed agents, Connectivity-preserving flocking algorithm, Connectivity-preserving flocking algorithm with bounded potential function, Adaptive flocking algorithms with nonlinear dynamics
  • Time-delay in multi-agent systems:Basic definitions, Types of time-delays in multi-agent systems, Analysis techniques (Frequency-domain techniques, Techniques based on Lyapunov-krasovaskii function (LMI tool), Techniques based on Stochastic matrix theory), synthesis and analysis of delayed consensus protocols in switching networks (with time-varying 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, continuous-time mean square average-consensus (with measurement noises, with measurement noises and time-varying communication time-delays, with measurement noises and arbitrary switching topology

Text Book:

  • 1- Distributed Coordination of Multi-agent Networks: Emergent problems, Models and Issues, by Wei Ren, Yongcan Cao, Communications and Control Engineering Series, Springer-Verlag, London, 2011.
  • 2- Distributed Consensus in Multi-Vehicle Cooperative Control: Theory and Applications, by Wei Ren and Randal W. Beard, Communications and Control Engineering Series, Springer-Verlag, 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, Jordan-form 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, Jordan-form 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(* C-T 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:

    "
  • 1-

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 N-dimensional 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, input-output representation of linear systems (transfer function, transmission zeros, transfer function poles), Linear system properties, Time-domain solution of LTI state equations
  • computing methods for state transition matrix (Laplace method, Caley-Hamilton method, Silvester method, Jordan form method), Similarity transformation, diagonal form, Block-diagonal 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 pole-zero 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 Time-varying (LTV) systems: Fundamental matrix, State transition matrix, solution of LTV system, Equivalent LTV equations, Time-varying 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): full-order observer, Reduced-order observer, State feedback based controller with full-order observer, Separation property, Regulation and tracking, Tracking with disturbance rejection, State feedback based controller with reduced-order observer
  • 10- Introduction to optimal control systems: Formulation of optimal control problem, LQR optimal feedback gain computation "


 Modern Control(* C-T 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:

    "
  • 1-

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 N-dimensional 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, input-output representation of linear systems (transfer function, transmission zeros, transfer function poles), Linear system properties, Time-domain solution of LTI state equations
  • computing methods for state transition matrix (Laplace method, Caley-Hamilton method, Silvester method, Jordan form method), Similarity transformation, diagonal form, Block-diagonal 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 pole-zero 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 Time-varying (LTV) systems: Fundamental matrix, State transition matrix, solution of LTV system, Equivalent LTV equations, Time-varying 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): full-order observer, Reduced-order observer, State feedback based controller with full-order observer, Separation property, Regulation and tracking, Tracking with disturbance rejection, State feedback based controller with reduced-order observer "


 
 
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