Gradient-based Numerical Solution To Optimal Control Of Hybrid Systems And Its Application

Hybrid systems exist extensively in daily life and industrial processes. Researchers in every field have made a lot of work for hybrid systems, optimal control of hybrid systems is one of the most important contents among all. It has both great theoretical significance and extensive engineering application background. For deterministic hybrid systems with a prespecified mode switching order, control constraints, state jumps and mode invariants, this thesis proposes an effective numerical algorithm to obtain the global optimal solution of optimal control problems. And quality control problem of injection molding products is also studied using the proposed numerical algorithm.The research results of this thesis mainly include the following three aspects:1) For optimal control problem of deterministic hybrid systems with a prespecified mode switching order, control constraints, state jumps and mode invariants, a numerical algorithm based on gradient information is presented. Firstly extend the Maximum Principle for such optimal control problems and obtain the oplimality conditions. Then based on optimality conditions, the gradient formulas of the objective function with respect to control variables are established by sensitivity analysis. Through control vector parameterization method the optimization problem of such hybrid systems can be converted to a finite dimensional nonlinear programming problem, which can be solved by gradient-based algorithm. Moreover, to avoid the singular Jacobian problem encountered in the process of finding numerical solution, we propose an improved method so that numerical solution to optimal control of such hybrid systems can be successfully obtained.2) From the perspective of getting global optimal solution, the filled function method is first introduced for optimal control of hybrid systems, and then a numerical algorithm combined filled function method and gradient-based algorithm is proposed. This algorithm consists of two phases:local minimization (a local minimizer is found by gradient-based algorithm) and filling (a filled function is constructed to find a local smaller minimizer); the two phases are repeated until the global minimizer is found.3) Quality control problem of injection molding products is studied using the numerical algorithm for optimal control of hybrid systems. The theory of hybrid systems is applied in injection molding process, and for control problem of injection molding products we apply the acquired research achievement——numerical algorithm for optimal control of hybrid systems to obtain its inputs which can produce the products with best quality. We choose injection velocity, packing pressure and filling-to-packing switchover as control variables, product weight as quality specification. Conduct experiments in the injection molding machine, and collect experiment data. According to these experiment data, hybrid system model for injection molding process and optimal problem of product quality control are built. Finally the numerical algorithm is used to solve the optimal control problem, which helps us obtain the optimal curvilinear paths of injection velocity and packing pressure, and optimal filling-to-packing switchover.