Optimal Control Approach For Nonlinear System With Switching Structure

In this dissertation, optimal control theory and applications of nonlinear system with switching structure in finite horizon are researched,and main contributions are summarized as follows:The subsection gradient method is proposed to optimize the switching times for Bang-Bang control laws. The time horizon is partitioned into several subintervals according to control switching times, and the time segments are defined as optimization parameters. By introducing a normalized time variable, free time interval is converted into a fixed one. The adjoint functions are solved to obtain the gradients of objective functions. Several numerical examples show the effectiveness of the subsection gradient method for solving the Bang-Bang control problems.A method for optimization with respect to the switching times of controls containing both Bang-Bang and singular arcs is presented. The problem is partitioned as several stages, with each stage corresponding to a particular control arc. The control functions on the singular intervals are approximated by a linear combination of B-splines, and the problem is converted to a static nonlinear programming problem. The control profiles and stage lengths act as decision variables. A multi-stage adjoint system is constructed to calculate the gradients. The numerical solution is obtained by using the sequential quadratic programming method.A class of optimal control problem for switching systems with prespecified order of the sequence of subsystems is numerically solved based on piecewise linear parameterization method and the proposed subsection gradient method. The time horizon is partitioned into several subintervals according to the number of subsystems and the state equation is different in every subinterval. The optimal control problem of switching system is converted into a nonlinear multi-stage dynamic optimization problem. Both time-varying and time-invariant cases are studied. Three examples are solved using the proposed method so as to demonstrate it's effectiveness.An optimal control model of a multi-stage jump transition hybrid dynamical system with jump transition constraints is established. The necessary conditions of the optimal control problem for multi-stage jump transition hybrid system were deduced by using calculus of variations, and the jump transition influence on the optimal control is put forward. A control problem for two-stage reactor system is solved to demonstrate the effectiveness of this approach.A hybrid genetic algorithm (GA) is proposed which can be used to solve the nonlinear programming problem. This hybrid algorithm refers to the position displacement strategy of the particle swarm optimization (PSO) and makes use of the gauss PSO to improve the mutation operation of the GA. The hybrid GA is tested with three benchmark functions and applied to solve heat transfer and time optimal control problems. The result of the test and application shows that this hybrid GA is efficient to solve the nonlinear programming problems.