Switched Optimal Control And Hybrid Dynamical System Identification Based On Parallel Technique

In recent years, a class of systems which contains both continuous dynamics and discrete events have attracted many researchers due to its wide range of applications and inherent com-plexity with the result that the research has been a new topic for it. These systems are called as hybrid systems. Under the framework of hybrid systems, two classes of problems that need to be worked out are studied in this dissertation. For one thing, a class of optimal control problem-s for switching systems is studied without imposing restrictions on the mode sequence or the number of mode switchings. For another, this dissertation investigates a class of nonlinear hy-brid systems and their system identification based on the background of microbial production of1,3-propanediol. Under the support of the two National Natural Science Foundations of China, this research can not only develop the optimal control theory and optimization algorithm, but also provide certain reference for the practical applications. Therefore, it is very interesting both in theory and in practice. The main contributions obtained in this dissertation are summarized as follows.1. Under the conditions that the mode sequence and the number of mode switchings are not pre-specified, this dissertation considers a class of optimal switching control problems with the general convex compact constraints involving a switched system composed of s (s≥2) subsystems. We formulate an embedded system, and further construct a relaxed system. The relationships between trajectories of these systems and the switched system are discussed by a constructive method, and the suboptimal solutions of switched optimal control are constructed. According to the Maximum Principle, a few conditions are developed for judging optimal or suboptimal solutions of the switched system based on the necessary conditions for optimality of the embedded system. On the basis of the conditions, a solving method for optimal or suboptimal solutions is given. Furthermore, we provide a numerical algorithm for determining optimal or suboptimal solutions on the basis of parallel principle. The examples are computed applying the proposed algorithm on a Lenovo DeepComp1800PC-cluster Server, and the numerical results show the effectiveness of the proposed algorithm. 2. Taking the particular nature of constraint problems into consideration, this dissertation studies a class of switched optimal control problems with the state, control and terminal con-straints, in which the mode sequence or the number of mode switchings are not also pre-specified as well. Similar to the preceding, we reconstruct an embedded system, and the boundary condi-tions for the state constraint are discussed. The control regions for the switched system, switched subsystems and embedded system combining with the effective control region for the embedded system are defined. On the basis of the control regions, the relationships between trajectories of the switched system and embedded system with the constraint conditions are discussed, and therefore a construction method for the suboptimal solutions of switched optimal control prob-lem is given. Under the constraint conditions, the necessary conditions for optimality of the embedded system and the relationships between the optimal solutions of switched system and embedded system are discussed. We transform the problem with state constraints into the one with the general convex compact constraints by limiting control inputs of the embedded sys-tem in the effective control region so that a solving method with constraint is obtained. The illustrations show the effectiveness of the proposed algorithm.3. Based on the microbial continuous culture, since the metabolic mechanisms are still unclear in the process of fermentation of glycerol to1,3-propanediol, we consider the possible ways that the substrate and production pass the membrane and the possible ways that the in-termediate metabolic production inhibits both the cells and intracellular enzymes. Combining various possible transport and inhibition mechanisms, we give a nonlinear hybrid dynamical system model composed of72possible metabolic pathways which are described by an eight-dimensional differential equation involving discrete and continuous variables. The properties of solutions to the system are explored. Under the lack of intracellular experimental results, a pathway identification model is proposed for the complex metabolic system using the biological robustness of the intracellular substances and the measured experimental data of the extracel-lular substances. The model includes43848continuous variables and1152discrete variables. Considering the non-differentiable vector field and the large scale of problem, this dissertation provides a parallel particle swarm optimization-pathway identification algorithm (PPSO-PIA). Applying the proposed algorithm, we obtain an optimal pathway and the parameters, in which77172480numerical computations of differential equations are involved on Lenovo DeepComp1800PC-cluster Server. The obtained optimal pathway can describe the continuous fermen- tation reasonably, and the results provide a important reference for conjecturing fermentation mechanisms.