Modern Control Theory I.

I. Discrete time control of single variable (SISO) systems

• Two deree of freedom (2DOF) control design based on reference model.
  
• Control design for dead time systems using Smith predictor.
• k-step ahead predictor.
• Generalized predictive control.
  

• Controllability, reachability, observability, reconstructability. Canonical forms. Algebraic  similarity of continuous time and discrete time systems.
• Pole assignment using state feedback. Full and minimal order state observers.
• Generalized predictive control in state space.
• Decoupling with stability guarantee.

III. Nonlinear control systems

• Stability (Lyapunov, asymptotic, global).
• Lyapunov’s direct method. Lyapunov’s indirect method. LaSalle theorem.
• Sliding mode control, elimination of oscillations.
• Backstepping control. Input/state linearization.

 IV. Optimal control systems

•  Analytical conditions of static optimum. Karush-Kuhn-Tucker theorem. Lagrange multiplier rule.

• Numerical optimization methods in finite dimension. Optimum seeking in a single variable. Gradient, conjugate gradient, Newton and quasi-Newton methods. Davidon-Fletcher-Powell (DFP) and Broyden-Fletcher-Goldfarb-Shanno (BFGS) methods.
• Discrete time LQ control of LTV systems. Reciprocal roots condition for LTI systems, solution based on  eigenvalue/eigenvector technique and algebraic Riccati equation (DARE).
• Kalman filter for LTV stochastic systems. Similarity to LQ control. Kalman filter for LTI systems. LQG control. Extended Kalman Filter (EKF) for nonlinear systems.
• Analytical conditions of dynamic optimum. Local maximum principle. Pontrayagin’s maximum principle, bang-bang control.
• Continuous time LQ control of LTV systems. Symmetric roots condition for LTI systems, solution using eigenvalue/eigenvector technique and CARE.

 V. Identification and adaptive control

• Linear parameter estimation without and with forgetting. Batch and recursive algorithms. Nonlinear parameter estimation.
• Typical system and noise models. Cost function and its first and approximating second derivatives.
• Parameter estimation of ARX models using LS and IV (instrumental variable) methods.
• Parameter estimation of ARMAX model using numerical optimization based on quasi-Newton method.
• Identification of MIMO systems in state space. Hankel-parameters, shift invariance of generalized observability matrix. Linear algebra tools for solving N4SID and MOESP identification.
• Model predictive and selftuning adaptive control structures. Implicit (inverse) adaptive control of MIMO LTI systems.

 VI. Soft computing methods in control engineering

• Classification of neural networks (NN). Modeling of linear systems with time delay and feedforward neural networks (FFNN). Tuning of FFNNs, the BP (backpropagation) algorithm.
• Fuzzy sets and fuzzy set operations. Fuzzy logic, relations and implication algorithms. Defuzzyfications methods.  TSK, Sugeno and Wang type fuzzy systems.
• Fuzzy logic controllers. MacVicar-Whelan metarules. The rule base of fuzzy PD and PI type controllers. Fuzzy toolbox.
• Genetic algorithms (GA). Genotype and fenotype forms. Structure of simple and multipopulation genetic algorithms (SGA, MPGA). Fitness functions. Selection methods. Binary and real realizations of genetic operators. Reinsertion strategies. GA toolbox.
• Clastering. Structure estimation and system initialization.

VII. Adaptive fuzzy control

• Adaptive networks, ANFIS. Hybrid tuning of Sugeno controllers.
• Fuzzy SISO adaptive control. Structure of 1^st type indirect fuzzy control. Specifications and design prescriptions, Lyapunov equation. The form of the nominal and supervisory fuzzy controllers. Consideration of parameter constraints, Luenberger projection.
• Handling of the 2^nd type indirect fuzzy adaptive control. Stability guarantee and chance.
• Fuzzy approximation using SVF technique in two and more variables.