Finite-dimensional optimal controllers for nonlinear plants

Optimal risk sensitive feedback controllers are now available for very general stochastic nonlinear plants and performance indices. They consist of nonlinear static feedback of so called information states from an information state filter. In general, these filters are linear, but infinite dimensional, and the information state feedback gains are derived from (doubly) infinite dimensional dynamic programming. The challenge is to achieve optimal finite dimensional controllers using finite dimensional calculations for practical implementation.This paper derives risk sensitive optimality results for finite-dimensional controllers. The controllers can be conveniently derived for ‘linearized’ (approximate) models (applied to nonlinear stochastic systems). Performance indices for which the controllers are optimal for the nonlinear plants are revealed. That is, inverse risk-sensitive optimal control results for nonlinear stochastic systems with finite dimensional linear controllers are generated. It is instructive to see from these results that as the nonlinear plants approach linearity, the risk sensitive finite dimensional controllers designed using linearized plant models and risk sensitive indices with quadratic cost kernels, are optimal for a risk sensitive cost index which approaches one with a quadratic cost kernel. Also even far from plant linearity, as the linearized model noise variance becomes suitably large, the index optimized is dominated by terms which can have an interesting and practical interpretation.Limiting versions of the results as the noise variances approach zero apply in a purely deterministic nonlinear H_∞ setting. Risk neutral and continuous-time results are summarized.More general indices than risk sensitive indices are introduced with the view to giving useful inverse optimal control results in non-Gaussian noise environments.     

Output feedback control of switched nonlinear systems using multiple Lyapunov functions

This work presents a hybrid nonlinear control methodology for a broad class of switched nonlinear systems with input constraints. The key feature of the proposed methodology is the integrated synthesis, via multiple Lyapunov functions, of “lower-level” bounded nonlinear feedback controllers together with “upper-level” switching laws that orchestrate the transitions between the constituent modes and their respective controllers. Both the state and output feedback control problems are addressed. Under the assumption of availability of full state measurements, a family of bounded nonlinear state feedback controllers are initially designed to enforce asymptotic stability for the individual closed-loop modes and provide an explicit characterization of the corresponding stability region for each mode. A set of switching laws are then designed to track the evolution of the state and orchestrate switching between the stability regions of the constituent modes in a way that guarantees asymptotic stability of the overall switched closed-loop system. When complete state measurements are unavailable, a family of output feedback controllers are synthesized, using a combination of bounded state feedback controllers, high-gain observers and appropriate saturation filters to enforce asymptotic stability for the individual closed-loop modes and provide an explicit characterization of the corresponding output feedback stability regions in terms of the input constraints and the observer gain. A different set of switching rules, based on the evolution of the state estimates generated by the observers, is designed to orchestrate stabilizing transitions between the output feedback stability regions of the constituent modes. The differences between the state and output feedback switching strategies, and their implications for the switching logic, are discussed and a chemical process example is used to demonstrate the proposed approach.     

具有传感器故障的非线性关联大系统的可靠控制

考虑一类非线性关联大系统的可靠控制器设计问题,该系统具有常时滞、参数不确定性、非线性扰动和传感器故障.其中参数不确定性满足匹配条件,非线性扰动满足范数有界条件,传感器具有部分失效的模型.本文的目的是设计无记忆分散控制器来镇定该系统.通过解线性矩阵不等式获得此控制器,使得当传感器器发生故障时被控系统能够保持渐近稳定.最后通过仿真的例子,验证该状态反馈控制器的可行性.     

A Remark on Sensor Disturbance Rejection of Nonlinear Systems

When disturbances enter sensors, the states of a plant cannot be precisely measured and the state feedback controllers are not implementable. Instead, the so-called measurement feedback controllers become interesting. For nonlinear systems, the output regulation theory is widely used for handling actuator and plant disturbances. This note gives a remark how the output regulation theory can be applied for sensor disturbances, and hence provides a novel measurement feedback design approach.     

Rough controllers with state feedback

This paper addresses a new approach to design rule-based controllers using concepts of rough sets and techniques of state feedback. The goal is to obtain rule-based models that allow the construction of control loops, ensuring stable conditions and suitable dynamic characteristics for nonlinear systems. The study performs a comparison of the procedure proposed with results obtained with a conventional control, where a system with nonlinear behavior is used. Numerical examples derived from computer simulations and real applications are shown. Experiments in a level plant were performed, checking the potential of the rule-based controllers.     

Robust output tracking for uncertain/nonlinear systems subject to almost constant disturbances

In this paper, we consider uncertain/nonlinear systems subject to unknown constant disturbance inputs. We wish to design state feedback controllers which ensure that the system output asymptotically tracks a specified constant reference signal and all states are bounded. The controllers we consider are PI in the sense that they consist of a piece which depends linearly on the state and another piece which depends on the integral of the output tracking error. Our main result reduces the original problem to a stabilization problem for an associated augmented system which we call the derivative augmented system. We obtain controller design procedures for specific classes of uncertain/nonlinear systems. Then we extend these results to the situation in which the reference signal and the disturbance are not necessarily constant but asymptotically approach a constant.     

Nonlinear H/sub /spl infin// controllers for electromagnetic suspension systems

This note presents a unified framework to derive nonlinear H/sub /spl infin// state and output feedback controllers for magnetically levitated (Maglev) vehicles with controlled dc electromagnets, referred to as electromagnetic suspension systems. The theoretical exposition, based on the Taylor series expansion solution to the Hamilton-Jacobi-Isaacs inequality, is followed by an assessment of some of the practical issues in realizing the nonlinear controllers with a digital signal processor and embedded hardware. A select set of experimental results from a single-degree-of-freedom suspension system is included to highlight the effectiveness of the proposed nonlinear stateand output-feedback H/sub /spl infin// controllers to suppress guideway-induced disturbances.     

LPV controller design for the nonlinear RTAC system

This paper proposes three kinds of state‐feedback controllers for the nonlinear rotational and translational actuator (RTAC) benchmark problem. Interpolating a nonlinear system into an LPV system associated with time‐varying and state‐dependent weighting functions allows one to apply various linear system theories and techniques for analysing and synthesizing nonlinear systems, and thus to generate LMI criteria to supply various stabilizers and guaranteed cost controllers. This approach is more flexible for this benchmark problem than existing approaches in the literature because the other controllers excessively depend on the structure of the nonlinear system. Simulation results show the performance of the resulting controllers. Copyright © 2001 John Wiley & Sons, Ltd.     

Simultaneous $H^{infty}$ Control for Nonlinear Systems

This note develops a novel method for designing simultaneous $H^{infty}$ state feedback controllers for a collection of single-input nonlinear systems. Based on the Kalman—Yakubovich—Popov Lemma, necessary and sufficient conditions for the existence of simultaneous $H^{infty}$ controllers are derived by the control storage function approach. A universal formula for constructing continuous, time-invariant, simultaneous $H^{infty}$ state feedback controllers is presented.      

A compact design scheme of adaptive output-feedback control for uncertain nonlinear systems

Multiple uncertainties/noises, frequently exist in a plant, usually require multiple compensation techniques, which renders feedback controllers highly dynamic and nonlinear. This motivates us to search for a compact design scheme of compensation to reduce the complexity of controllers. In this paper, global output-feedback stabilisation is investigated for a class of uncertain nonlinear systems with unknown unmeasured states-dependent growth and input matching uncertainty. To solve the problem, a compact scheme is proposed to design a global adaptive output-feedback controller, which combines the technique of dynamic gain and extended state observer together. Particularly, only one dynamic gain, rather than two dynamic gains, is introduced to deal with the unknown polynomial-of-output growth rate, which makes our controller to have lower dynamics than those in the related works. Moreover, the input matching uncertainty is asymptotically estimated by the extended state observer, and thus its effect is well counteracted. It is shown that, under the designed controller, the system states globally converge to zero. A simulation example on non-zero set-point regulation demonstrates the effectiveness of the proposed approach.