Robust nonlinear control of vectored thrust aircraft

An interdisciplinary program in robust control for nonlinear systems with applications to a variety of engineering problems is outlined. Major emphasis will be placed on flight control, with both experimental and analytical studies. This program builds on recent new results in control theory for stability, stabilization, robust stability, robust performance, synthesis, and model reduction in a unified framework using Linear Fractional Transformations (LFT's), Linear Matrix Inequalities (LMI's), and the structured singular value micron. Most of these new advances have been accomplished by the Caltech controls group independently or in collaboration with researchers in other institutions. These recent results offer a new and remarkably unified framework for all aspects of robust control, but what is particularly important for this program is that they also have important implications for system identification and control of nonlinear systems. This combines well with Caltech's expertise in nonlinear control theory, both in geometric methods and methods for systems with constraints and saturations

Unknown dynamics estimator-based output-feedback control for nonlinear pure-feedback systems

Most existing adaptive control designs for nonlinear pure-feedback systems have been derived based on backstepping or dynamic surface control (DSC) methods, requiring full system states to be measurable. The neural networks (NNs) or fuzzy logic systems (FLSs) used to accommodate uncertainties also impose demanding computational cost and sluggish convergence. To address these issues, this paper proposes a new output-feedback control for uncertain pure-feedback systems without using backstepping and function approximator. A coordinate transform is first used to represent the pure-feedback system in a canonical form to evade using the backstepping or DSC scheme. Then the Levant's differentiator is used to reconstruct the unknown states of the derived canonical system. Finally, a new unknown system dynamics estimator with only one tuning parameter is developed to compensate for the lumped unknown dynamics in the feedback control. This leads to an alternative, simple approximation-free control method for pure-feedback systems, where only the system output needs to be measured. The stability of the closed-loop control system, including the unknown dynamics estimator and the feedback control is proved. Comparative simulations and experiments based on a PMSM test-rig are carried out to test and validate the effectiveness of the proposed method

ADAPTIVE DYNAMICAL FEEDBACK REGULATION STRATEGIES FOR LINEARIZABLE UNCERTAIN SYSTEMS

In this paper we address the design of adaptive dynamical feedback strategies of the continuous and discontinuous, types for the output stabilization of nonlinear systems. The class of systems considered corresponds to nonlinear controlled systems exhibiting linear parametric uncertainty. Dynamical feedback controllers, ideally achieving output stabilization via exact linearization, are obtained by means of repeated output differentiation and, either, pole placement, or, sliding mode control techniques. The adaptive versions of the dynamical stabilizing controllers are then obtainable through standard, direct, overparamemzed adaptive control strategies available for linearizable systems. Illustrative examples are provided which deal with the regulation of electromechanical systems

Asymptotic Tracking Control of Uncertain MIMO Nonlinear Systems with Less Conservative Controllability Conditions

For uncertain multiple inputs multi-outputs (MIMO) nonlinear systems, it is nontrivial to achieve asymptotic tracking, and most existing methods normally demand certain controllability conditions that are rather restrictive or even impractical if unexpected actuator faults are involved. In this note, we present a method capable of achieving zero-error steady-state tracking with less conservative (more practical) controllability condition. By incorporating a novel Nussbaum gain technique and some positive integrable function into the control design, we develop a robust adaptive asymptotic tracking control scheme for the system with time-varying control gain being unknown its magnitude and direction. By resorting to the existence of some feasible auxiliary matrix, the current state-of-art controllability condition is further relaxed, which enlarges the class of systems that can be considered in the proposed control scheme. All the closed-loop signals are ensured to be globally ultimately uniformly bounded. Moreover, such control methodology is further extended to the case involving intermittent actuator faults, with application to robotic systems. Finally, simulation studies are carried out to demonstrate the effectiveness and flexibility of this method

Leader-following consensus for lower-triangular nonlinear multi-agent systems with unknown controller and measurement sensitivities

summary:In this paper, a novel consensus algorithm is presented to handle with the leader-following consensus problem for lower-triangular nonlinear MASs (multi-agent systems) with unknown controller and measurement sensitivities under a given undirected topology. As distinguished from the existing results, the proposed consensus algorithm can tolerate to a relative wide range of controller and measurement sensitivities. We present some important matrix inequalities, especially a class of matrix inequalities with multiplicative noises. Based on these results and a dual-domination gain method, the output consensus error with unknown measurement noises can be used to construct the compensator for each follower directly. Then, a new distributed output feedback control is designed to enable the MASs to reach consensus in the presence of large controller perturbations. In view of a Lyapunov function, sufficient conditions are presented to guarantee that the states of the leader and followers can achieve consensus asymptotically. In the end, the proposed consensus algorithm is tested and verified by an illustrative example

SMC design for robust H∞ control of uncertain stochastic delay systems

Recently, sliding mode control method has been extended to accommodate stochastic systems. However, the existing results employ an assumption that may be too restrictive for many stochastic systems. This paper aims to remove this assumption and present in terms of LMIs a sliding mode control design method for stochastic systems with state delay. In some cases, the proposed method provides a control scheme for finite-time stabilization of stochastic delay systems

Adaptive and non-adaptive control without identification: a survey

Three related but distinct scenarios for tracking control of uncertain systems are reviewed: asymptotic tracking, approximate tracking with prescribed asymptotic error bound, tracking with prescribed transient behaviour. A variety of system classes are considered, ranging from finite-dimensional linear minimum-phase systems to nonlinear, infinite-dimensional systems described by functional differential equations. These classes are determined only by structural assumptions, such as stable zero dynamics and known relative degree. The objective is a single (and simple) control structure which is effective for every member of the underlying system class: no attempt is made to identify the particular system being controlled

Optimal Pole Assignment of Linear Systems by the Sylvester Matrix Equations

The problem of state feedback optimal pole assignment is to design a feedback gain such that the closed-loop system has desired eigenvalues and such that certain quadratic performance index is minimized. Optimal pole assignment controller can guarantee both good dynamic response and well robustness properties of the closed-loop system. With the help of a class of linear matrix equations, necessary and sufficient conditions for the existence of a solution to the optimal pole assignment problem are proposed in this paper. By properly choosing the free parameters in the parametric solutions to this class of linear matrix equations, complete solutions to the optimal pole assignment problem can be obtained. A numerical example is used to illustrate the effectiveness of the proposed approach

Fixed-time Stabilization with a Prescribed Constant Settling Time by Static Feedback for Delay-Free and Input Delay Systems

A static non-linear homogeneous feedback for a fixed-time stabilization of a linear time-invariant (LTI) system is designed in such a way that the settling time is assigned exactly to a prescribed constant for all nonzero initial conditions. The constant convergence time is achieved due to a dependence of the feedback gain of the initial state of the system. The robustness of the closed-loop system with respect to measurement noises and exogenous perturbations is studied using the concept of Input-to-State Stability (ISS). Both delay-free and input delay systems are studied. Theoretical results are illustrated by numerical simulations