Chengzhi Yuan

Hybrid Control for Switched Linear Systems with Average Dwell Time

This technical note presents a hybrid control scheme for the output-feedback control of switched linear systems with average dwell time. The proposed hybrid controller consists of a standard switching output-feedback control law and a supervisor enforcing a reset rule for the switching controller states at each switching instant. This hybrid control scheme provides an efficient and systematic way for designing average dwell time switched linear control systems in the sense that the boundary condition can be incorporated into the synthesis problem in a convex formulation. Specifically, both full-order and reduced-order controllers with guaranteed stability and optimal weighted H∞ performance will be solved by linear matrix inequality (LMI) optimizations. Simulation studies are included to illustrate the effectiveness of the proposed approach.

Switching control of linear systems subject to asymmetric actuator saturation

In this paper, we study the saturation control problem for linear time-invariant (LTI) systems subject to asymmetric actuator saturation under a switching control framework. The LTI plant with asymmetric saturation is first transformed to an equivalent switched linear model with each subsystem subject to symmetric actuator saturation, based on which a dwell-time switching controller augmented with a controller state reset is then developed by using multiple Lyapunov functions. The controller synthesis conditions are formulated as linear matrix inequalities (LMIs), which can be solved efficiently. Simulation results are also included to illustrate the effectiveness and advantages of the proposed approach.

Persistency of excitation and performance of deterministic learning

Recently, a deterministic learning theory was proposed for locally-accurate identification of nonlinear systems. In this paper, we investigate the performance of deterministic learning, including the learning speed and learning accuracy. By analyzing the convergence properties of a class of linear time-varying (LTV) systems, explicit relations between the persistency of excitation (PE) condition (especially the level of excitation) and the convergence properties of the LTV systems are derived. It is shown that the learning speed increases with the level of excitation and decreases with the upper bound of PE. The learning accuracy also increases with the level of excitation, in particular, when the level of excitation is large enough, locally-accurate learning can be achieved to the desired accuracy, whereas low level of PE may result in the deterioration of the learning performance. This paper reveals that the performance analysis of deterministic learning can be established on the basis of classical results on stability and convergence of adaptive control. Simulation studies on the Moore-Greitzer model, a well-known axial flow compressor model, are included to illustrate the effectiveness of the results.

Asynchronous switching output feedback control of discrete-time switched linear systems

In this paper, the problem of dynamic output-feedback control synthesis is addressed for discrete-time switched linear systems under asynchronous switching. The proposed hybrid controller consists of a standard dynamic output-feedback switching control law and an impulsive reset law induced by controller state jumps. Using the average dwell time technique incorporating with multiple quadratic Lyapunov functions, the switching control synthesis conditions for asymptotic stability with guaranteed weighted ℓ2-gain performance are derived as a set of linear matrix inequalities (LMIs). The proposed hybrid synthesis scheme advances existing design methods for output-feedback asynchronous switching control of switched linear systems in two important aspects: LMI formulation of the synthesis problem; and arbitrary order of the controller state. A numerical example is used to illustrate the effectiveness and advantages of the proposed design technique.

Dynamic IQC-Based Control of Uncertain LFT Systems With Time-Varying State Delay

This paper presents a new exact-memory delay control scheme for a class of uncertain systems with time-varying state delay under the integral quadratic constraint (IQC) framework. The uncertain system is described as a linear fractional transformation model including a state-delayed linear time-invariant (LTI) system and time-varying structured uncertainties. The proposed exact-memory delay controller consists of a linear state-feedback control law and an additional term that captures the delay behavior of the plant. We first explore the delay stability and the L2-gain performance using dynamic IQCs incorporated with quadratic Lyapunov functions. Then, the design of exact-memory controllers that guarantee desired L2-gain performance is examined. The resulting delay control synthesis conditions are formulated in terms of linear matrix inequalities, which are convex on all design variables including the scaling matrices associated with the IQC multipliers. The IQC-based exact-memory control scheme provides a novel approach for delay control designs via convex optimization, and advances existing control methods in two important ways: 1) better controlled performance and 2) simplified design procedure with less computational cost. The effectiveness and advantages of the proposed approach have been demonstrated through numerical studies.

Hybrid Switched Gain-Scheduling Control for Missile Autopilot Design

This paper presents a new hybrid switched gain-scheduling control method for missile autopilot design via dynamic output feedback. For controller design purpose, the nonlinear missile plant model is first converted to a switched linear fractional transformation system. Then, the new hybrid switched gain-scheduling autopilot is designed, which consists of a switching dynamic output–feedback linear fractional transformation controller and a supervisor enforcing a controller state reset at each switching time instant. The proposed hybrid control scheme is shown to provide a systematic yet simple framework for missile autopilot design. Specifically, the control synthesis conditions that guarantee weighted L2 stability performance are formulated in terms of a finite number of linear matrix inequalities, which can be solved effectively via convex optimization without parameter-space gridding. Furthermore, stringent controlled performance and strong robustness against parameter perturbations are achieved using t...

Exact-memory and memoryless control of linear systems with time-varying input delay using dynamic IQCs

Input delay is an important type of actuator nonlinearity in control systems. In this paper, we will address the output-feedback control synthesis problem for linear systems with time-varying input delay under the integral quadratic constraint (IQC) framework. A new exact-memory control scheme is first proposed, which consists of a standard linear output-feedback control law and an internal delay loop. The delay loop is embedded in the controller structure so as to reproduce the input delay behavior of the plant. By using quadratic Lyapunov functions incorporated with dynamic IQC multipliers, the resulting dynamic output-feedback delay control synthesis problem is fully characterized by a set of linear matrix inequalities (LMIs), which are convex on all design variables including the scaling factors associated with the IQC multipliers. Moreover, the corresponding result on memoryless control is also derived for the case when the plant input-delay information is not available for feedback control. An application to network systems has been used to illustrate the effectiveness and usefulness of the proposed approach.

Design and performance analysis of deterministic learning of sampled-data nonlinear systems

In this paper, we extend the deterministic learning theory to sampled-data nonlinear systems. Based on the Euler approximate model, the adaptive neural network identifier with a normalized learning algorithm is proposed. It is proven that by properly setting the sampling period, the overall system can be guaranteed to be stable and partial neural network weights can exponentially converge to their optimal values under the satisfaction of the partial persistent excitation (PE) condition. Consequently, locally accurate learning of the nonlinear dynamics can be achieved, and the knowledge can be represented by using constant-weight neural networks. Furthermore, we present a performance analysis for the learning algorithm by developing explicit bounds on the learning rate and accuracy. Several factors that influence learning, including the PE level, the learning gain, and the sampling period, are investigated. Simulation studies are included to demonstrate the effectiveness of the approach.

Almost output regulation of discrete-time switched linear systems

In this paper, we propose a new hybrid control approach for almost output regulation of a class of discrete-time switched linear systems with average dwell time (ADT). Both controlled plant and exosystem are described by switched linear systems. The proposed hybrid controller is constructed as a switching impulsive system, where the controller states will undergo impulsive jumps at each switching instant. By using the ADT technique incorporated with multiple quadratic Lyapunov functions, the hybrid synthesis conditions for almost output regulation with asymptotic stability and weighted ℋ∞ performance are formulated as a set of linear matrix equations and linear matrix inequalities (LMIs), which can be solved effectively. The proposed hybrid control method has been demonstrated through a numerical example.

Robust Control of Switched Linear Systems via Min of Quadratics

In this paper, we will investigate the robust switching control problem for switched linear systems by using a class of composite quadratic functions, the min (of quadratics) function, to improve performance and enhance control design flexibility. The robustness is reflected in two prospectives including the ℋ∞ performance and arbitrary switching of subsystems. A hysteresis min-switching strategy is employed to orchestrate the switching among a collection of controllers. The synthesis conditions for both state feedback and output feedback control problems are derived in terms of a set of linear matrix inequalities (LMIs) with linear search over scalar variables. The proposed min function based approach unifies the existing single Lyapunov function based method and multiple Lyapunov function based method in a general framework, and the derived LMI conditions cover the existing LMI conditions as special cases. Numerical studies are included to demonstrate the advantages of the proposed control design approach.Copyright