Predictive Controller Design And Performance Analysis For Hybrid Dynamical Systems

Many complex processes not only include continuous physical, chemical and biologic reaction, but also are influenced by logic constraints, switching between different operating modes and human command, exhibiting hybrid dynamical characteristics. A class of complex systems in which continuous dynamic behavior and discrete dynamic behavior interact are called hybrid dynamical systems. The nonlinearity and even nonsmoothness of hybrid dynamical systems in nature make the problems of controller design and analysis very difficult, especially the case with constraints. Predictive control can deal with constraints, uncertainties and time delays. Also, it has the tolerance of model applied for prediction and efficiency of finite receding horizon optimization. Therefore, this methodology provides an important way for the control of hybrid dynamical systems. In this dissertation, predictive control is employed for hybrid dynamical systems, and the controller synthesis, the solution of optimization and the analysis of system performance are studied. The main contents are as follows.Predictive controller design methods for discrete time piecewise linear (PWL) systems are studied in consideration of the modeling uncertainty and disturbances. For PWL systems with constraints and persistent, unknown but bounded disturbances, a constraints tightening robust predictive controller is presented. Based on optimization problem of predictive control for nominal PWL systems, the constraints are tightened to overcome the influence of persistent bounded disturbances. The proposed predictive controller can guarantee robust feasibility and convergence of closed-loop PWL systems, and reduce the complexity of computation. For uncertain structure of PWL systems that is described by a set of polytopic parameter varying models, an infinite horizon on-line predictive control technique for guaranteeing robust stability is developed by solving linear matrix matrices (LMIs). On the basis of the on-line algorithm, an improved algorithm is proposed to reduce computation.For continuous-time PWL systems, a mixed predictive control strategy is proposed to guarantee global stability. For each mode of PWL systems, a bounded controller and a predictive controller are designed respectively, and a stable estimation region of PWL systems is developed. In the stable estimation region, a mixed control switching strategy based on predictive control and bounded control is given for each mode to achieve the reconciliation of stability and optimality properties. With the switching rules of different modes of PWL systems, the global stability can be guaranteed. In the proposed method, only quadratic programming problems are computed, which reduces on-line complexity of the optimization of hybrid dynamical systems.As a class of hybrid dynamical systems, networked control systems (NCSs) include interacting discrete and continuous dynamical characteristics. Thus, hybrid systems control theory and approaches can be used in the control of NCSs. Using multirate scheme to describe NCSs can reduce the loss of information caused by network congestion, and can get a good response. For multirate networked control systems (MNCSs) with the output sampling period several times larger than the input updating period, we can use predictive control strategy to generate a set of future control sequences to compensate for the network-induced time delays. The closed-loop MNCSs are described as switched systems. Sufficient stability conditions are established via a switched Lyapunov function approach. Then, a predictive controller dependent on state for stabilizing MNCSs is proposed based on a finite input and state horizon cost with a finite terminal weighting matrix. Compared with traditional predictive control, the proposed stabilizing predictive control strategy can compensate for the influence of network-induced time delays.Limited capacity for transmission of NCSs can lead to network-induced time delays, data losses and other problems, which can reduce systems performance and even destabilize systems. In order to overcome these problems, there are two approaches: (i) The influence of network-induced time delays and data packet loss can be compensated by system synthesis. (ii) The communication property can be improved by reasonable allocation and scheduling of network communication resources. From the perspective of systems synthesis, a receding horizon state estimation is proposed for MNCSs to overcome the influence of network-induced time delays. Convergence results and unbiasedness properties are analyzed. An upper bound of estimation error is presented under the assumption of bounded disturbances acting on the system and measurement equations. Taking the influence of communication constraints into account, from the perspective of improving communication performance, a communication scheduling matrix is introduced to describe possible scheduling, and the closed-loop MNCSs can be modeled as mixed logic dynamical systems. A predictive controller is designed by solving a mixed integer quadratic programming problem, which not only can stabilize closed-loop systems but also can present dynamical scheduling of communication channels.