- to know the problems of unconstrained optimization and parametric optimization with restrictions for optimization parameters;
- to know the theoretical (analytical) optimization methods and methods of extremum search for real physical objects or their models;
- to be able to build the criteria, to formulate restrictions and to choose methods and algorithms for parametric optimization of control systems in order to obtain necessary quality parameters of control system;
- to know the scope of application of direct, gradient and pseudo-Newtonian methods and algorithms to find extremum;
- to know the methods and problems of optimal control for dynamic systems;
- to be able to apply the Matlab tools for optimization problems of objects and control systems;
- to be able to use Simulink Design Optimisation for optimization problems in dynamic systems.

Prerequisites:
- Further Mathematics, Parts 1, 2, 3;
- Modeling of Controlled Plants;
- Automatic Control Theory;
- Identification and Simulation of Technological Objects.

The problems of parametric optimization. The problems of synthesis of optimal control systems and their fundamental difference from the problems of parametric optimization. The criteria in problems of parametric optimization. The criteria in problems of optimal control. Classical methods. Methods of extremum search. Optimization criteria, optimization parameters. The problems of unconstrained optimization. Optimization problems with restrictions. Restrictions types. One-parameter and multi-parameter optimization problems. The structure of optimization problem. Classification of optimization problems. Methods of one-parameter optimization. The classic method. Minimax and approximation methods of optimization and their using conditions. Methods for unconstrained multi-parameter optimization. The classic method of multi-parameter optimization. Elements of field theory. Differential characteristics of scalar field. The gradient of scalar field. Differential characteristic of gradient vector field. Hessian matrix. The necessary and sufficient conditions for local extremum of function of many variables. The saddle points. Checking of Hessian matrix for positive determination. Computer tools for graphic interpretation of optimization problems. Methods of extremum search. Methods of search for multi-parameter optimization. Heuristic and theoretical methods of extremum search. Methods of direct search. Search along the direction. Gradient search techniques. The theoretical basis of quasi-Newton extremum search methods (methods of variable metric). Evaluation of methods for unconstrained optimization in terms of citation. MATLAB functions for solving the multi-parameter problems of unconstrained optimization and their methods. Nonlinear optimization with constraints. Classical methods of constrained optimization. Restrictions in the form of equations. The method of Lagrange multipliers. The necessary and sufficient conditions for optimality. Restrictions in the form of inequalities. The problem of nonlinear programming. Kuhn-Tucker conditions for optimality. Kuhn-Tucker problem. Methods of extremum search for problems with restrictions. Converting constrained optimization problem into a sequence of unconstrained optimization problems. Method of penalty functions. MATLAB functions for solving the problems of multi-parameter constrained optimization and their methods. Synthesis of optimal control systems. The standard form of linear systems. Controllability, recoverability and observability of systems. The problem of synthesis of the determined optimal linear regulator.

1. Bundy U. B. Optimization methods. Introduction. Publishing house “Radio and Communication”, Moscow, 1988, (in Russian);
2. G. V. Reklaitis, A. Ravindran, Ken M. Ragsdell, Engineering Optimization: Methods and Applications, 2nd Edition, 2006;
3. Kvakernaak X., Sivan R. Linear optimal control systems. - Moscow: Publishing house “Science”, 1977, (in Russian);
4. Feldbaum B. A. Basic theory of optimal control, Moscow: Publishing house “Science”, 1968, (in Russian).

- written reports on laboratory works, oral questioning, 30%;
- exam (written and oral form), 70%.

- to know the problems of unconstrained optimization and parametric optimization with restrictions for optimization parameters;
- to know the theoretical (analytical) optimization methods and methods of extremum search for real physical objects or their models;
- to be able to build the criteria, to formulate restrictions and to choose methods and algorithms for parametric optimization of control systems in order to obtain necessary quality parameters of control system;
- to know the scope of application of direct, gradient and pseudo-Newtonian methods and algorithms to find extremum;
- to know the methods and problems of optimal control for dynamic systems;
- to be able to apply the Matlab tools for optimization problems of objects and control systems;
- to be able to use Simulink Design Optimisation for optimization problems in dynamic systems.

Prerequisites:
- Further Mathematics, Parts 1, 2, 3;
- Modeling of Controlled Plants;
- Automatic Control Theory;
- Identification and Simulation of Technological Objects.

The problems of parametric optimization. The problems of synthesis of optimal control systems and their fundamental difference from the problems of parametric optimization. The criteria in problems of parametric optimization. The criteria in problems of optimal control. Classical methods. Methods of extremum search. Optimization criteria, optimization parameters. The problems of unconstrained optimization. Optimization problems with restrictions. Restrictions types. One-parameter and multi-parameter optimization problems. The structure of optimization problem. Classification of optimization problems. Methods of one-parameter optimization. The classic method. Minimax and approximation methods of optimization and their using conditions. Methods for unconstrained multi-parameter optimization. The classic method of multi-parameter optimization. Elements of field theory. Differential characteristics of scalar field. The gradient of scalar field. Differential characteristic of gradient vector field. Hessian matrix. The necessary and sufficient conditions for local extremum of function of many variables. The saddle points. Checking of Hessian matrix for positive determination. Computer tools for graphic interpretation of optimization problems. Methods of extremum search. Methods of search for multi-parameter optimization. Heuristic and theoretical methods of extremum search. Methods of direct search. Search along the direction. Gradient search techniques. The theoretical basis of quasi-Newton extremum search methods (methods of variable metric). Evaluation of methods for unconstrained optimization in terms of citation. MATLAB functions for solving the multi-parameter problems of unconstrained optimization and their methods. Nonlinear optimization with constraints. Classical methods of constrained optimization. Restrictions in the form of equations. The method of Lagrange multipliers. The necessary and sufficient conditions for optimality. Restrictions in the form of inequalities. The problem of nonlinear programming. Kuhn-Tucker conditions for optimality. Kuhn-Tucker problem. Methods of extremum search for problems with restrictions. Converting constrained optimization problem into a sequence of unconstrained optimization problems. Method of penalty functions. MATLAB functions for solving the problems of multi-parameter constrained optimization and their methods. Synthesis of optimal control systems. The standard form of linear systems. Controllability, recoverability and observability of systems. The problem of synthesis of the determined optimal linear regulator.

1. Bundy U. B. Optimization methods. Introduction. Publishing house “Radio and Communication”, Moscow, 1988, (in Russian);
2. G. V. Reklaitis, A. Ravindran, Ken M. Ragsdell, Engineering Optimization: Methods and Applications, 2nd Edition, 2006;
3. Kvakernaak X., Sivan R. Linear optimal control systems. - Moscow: Publishing house “Science”, 1977, (in Russian);
4. Feldbaum B. A. Basic theory of optimal control, Moscow: Publishing house “Science”, 1968, (in Russian).

- written reports on laboratory works, oral questioning, 30%;
- exam (written and oral form), 70%.