Robust Stabilization of Nonlinear Systems by Quantized and Ternary Control

Results on the problem of stabilizing a nonlinear continuous-time system by a finite number of control or measurement values are presented. The basic tool is a discontinuous version of the so-called semi-global backstepping lemma. We derive robust practical stabilizability results by quantized and ternary controllers and apply them to some significant control problems.Comment: 14 pages, 4 figure

Event-triggered dynamic output quantized control for 2-D switched systems

It is well known that designing mode-dependent event-triggered control (MDETC) brings challenging difficulties to theoretical analysis, especially for two-dimensional (2-D) switched systems. Therefore, for 2-D switched Fornasini–Marchesini local state-space (FMLSS) systems, this paper designs a MDETC to investigate global exponential stabilization almost surely (GES a.s.). A MDETC based on dynamic output quantization control scheme is designed, which not only has a wide range of practicability, but also greatly saves network bandwidth resources. By constructing mode-dependent Lyapunov functions that include two time directions, some novel sufficient conditions are provided such that the switched FMLSS system achieves GES a.s. Unlike most previous results, our results do not require each mode to be stable, not even after adding control. Finally, numerical experiments are provided to verify the validity of our main theoretical results

Limited-information control of hybrid systems via reachable set propagation

ABSTRACT This paper deals with control of hybrid systems based on limited information about their state. Specifically, measurements being passed from the system to the controller are sampled and quantized, resulting in finite data-rate communication. The main ingredient of our solution to this control problem is a novel method for propagating overapproximations of reachable sets for hybrid systems through sampling intervals, during which the discrete mode is unknown. In addition, slow-switching conditions of the (average) dwell-time type and multiple Lyapunov functions play a central role in the analysis

STABILITY AND PERFORMANCE OF NETWORKED CONTROL SYSTEMS

Network control systems (NCSs), as one of the most active research areas, are arousing comprehensive concerns along with the rapid development of network. This dissertation mainly discusses the stability and performance of NCSs into the following two parts. In the first part, a new approach is proposed to reduce the data transmitted in networked control systems (NCSs) via model reduction method. Up to our best knowledge, we are the first to propose this new approach in the scientific and engineering society. The "unimportant" information of system states vector is truncated by balanced truncation method (BTM) before sending to the networked controller via network based on the balance property of the remote controlled plant controllability and observability. Then, the exponential stability condition of the truncated NCSs is derived via linear matrix inequality (LMI) forms. This method of data truncation can usually reduce the time delay and further improve the performance of the NCSs. In addition, all the above results are extended to the switched NCSs. The second part presents a new robust sliding mode control (SMC) method for general uncertain time-varying delay stochastic systems with structural uncertainties and the Brownian noise (Wiener process). The key features of the proposed method are to apply singular value decomposition (SVD) to all structural uncertainties, to introduce adjustable parameters for control design along with the SMC method, and new Lyapunov-type functional. Then, a less-conservative condition for robust stability and a new robust controller for the general uncertain stochastic systems are derived via linear matrix inequality (LMI) forms. The system states are able to reach the SMC switching surface as guaranteed in probability 1 by the proposed control rule. Furthermore, the novel Lyapunov-type functional for the uncertain stochastic systems is used to design a new robust control for the general case where the derivative of time-varying delay can be any bounded value (e.g., greater than one). It is theoretically proved that the conservatism of the proposed method is less than the previous methods. All theoretical proofs are presented in the dissertation. The simulations validate the correctness of the theoretical results and have better performance than the existing results

State Estimation of Open Dynamical Systems with Slow Inputs: Entropy, Bit Rates, and relation with Switched Systems

Finding the minimal bit rate needed to estimate the state of a dynamical system is a fundamental problem. Several notions of topological entropy have been proposed to solve this problem for closed and switched systems. In this paper, we extend these notions to open nonlinear dynamical systems with slowly-varying inputs to lower bound the bit rate needed to estimate their states. Our entropy definition represents the rate of exponential increase of the number of functions needed to approximate the trajectories of the system up to a specified \eps error. We show that alternative entropy definitions using spanning or separating trajectories bound ours from both sides. On the other hand, we show that the existing definitions of entropy that consider supremum over all \eps or require exponential convergence of estimation error, are not suitable for open systems. Since the actual value of entropy is generally hard to compute, we derive an upper bound instead and compute it for two examples. We show that as the bound on the input variation decreases, we recover a previously known bound on estimation entropy for closed nonlinear systems. For the sake of computing the bound, we present an algorithm that, given sampled and quantized measurements from a trajectory and an input signal up to a time bound $T>0$, constructs a function that approximates the trajectory up to an \eps error. We show that this algorithm can also be used for state estimation if the input signal can indeed be sensed. Finally, we relate the computed bound with a previously known upper bound on the entropy for switched nonlinear systems. We show that a bound on the divergence between the different modes of a switched system is needed to get a meaningful bound on its entropy

Stability of quantized time-delay nonlinear systems: A Lyapunov-Krasowskii-functional approach

Lyapunov-Krasowskii functionals are used to design quantized control laws for nonlinear continuous-time systems in the presence of constant delays in the input. The quantized control law is implemented via hysteresis to prevent chattering. Under appropriate conditions, our analysis applies to stabilizable nonlinear systems for any value of the quantization density. The resulting quantized feedback is parametrized with respect to the quantization density. Moreover, the maximal allowable delay tolerated by the system is characterized as a function of the quantization density.Comment: 31 pages, 3 figures, to appear in Mathematics of Control, Signals, and System