严格反馈非线性系统预设性能backstepping 控制器设计

针对一类具有一般形式的严格反馈非线性系统,提出一种基于预设性能的backstepping控制器设计方法.所谓预设性能是指在保证跟踪误差收敛到一个预先设定的任意小的区域的同时,保证收敛速度及超调量满足预先设定的条件.首先引入性能函数的概念,通过误差转化将原始的受限系统转换为等价的非受限系统;然后基于Lyapunov理论进行backstepping控制器的设计,并进行了稳定性分析;最后通过仿真实验验证了所提出方法的正确性.     

Robust Adaptive Control of Feedback Linearizable MIMO Nonlinear Systems With Prescribed Performance

A novel robust adaptive controller for multi-input multi-output (MIMO) feedback linearizable nonlinear systems possessing unknown nonlinearities, capable of guaranteeing a prescribed performance, is developed in this paper. By prescribed performance we mean that the tracking error should converge to an arbitrarily small residual set, with convergence rate no less than a prespecified value, exhibiting a maximum overshoot less than a sufficiently small prespecified constant. Visualizing the prescribed performance characteristics as tracking error constraints, the key idea is to transform the ldquoconstrainedrdquo system into an equivalent ldquounconstrainedrdquo one, via an appropriately defined output error transformation. It is shown that stabilization of the ldquounconstrainedrdquo system is sufficient to solve the stated problem. Besides guaranteeing a uniform ultimate boundedness property for the transformed output error and the uniform boundedness for all other signals in the closed loop, the proposed robust adaptive controller is smooth with easily selected parameter values and successfully bypasses the loss of controllability issue. Simulation results on a two-link robot, clarify and verify the approach.     

Distributed low-complexity output feedback tracking control for nonlinear multi-agent systems with unmodeled dynamics and prescribed performance

This paper investigates the prescribed performance distributed output consensus problem under directed graphs. With the utilisation of a filter, the original system of each follower can be converted into a strict-feedback system. Then, we design a prescribed performance output feedback distributed control protocol by applying the backstepping approach in the converted system. The proposed protocol can guarantee that the consensus tracking error of each agent evolves in predefined decaying bounds to achieve the prescribed performance, that is, the consensus tracking error of each agent converges to a predetermined residual set at a convergence rate no less than a prespecified value and exhibiting a maximum overshoot less than a preassigned constant. Moreover, during the process of consensus, all the signals in the closed-loop system are globally uniformly bounded. A simulation example is given to verify the effectiveness of the proposed control protocol.     

Stabilization of max-plus-linear systems using model predictive control: The unconstrained case

Max-plus-linear (MPL) systems are a class of event-driven nonlinear dynamic systems that can be described by models that are “linear” in the max-plus algebra. In this paper we derive a solution to a finite-horizon model predictive control (MPC) problem for MPL systems where the cost is designed to provide a trade-off between minimizing the due date error and a just-in-time production. In general, MPC can deal with complex input and states constraints. However, in this paper we assume that these are not present and it is only required that the input should be a nondecreasing sequence, i.e. we consider the “unconstrained” case. Despite the fact that the controlled system is nonlinear, by employing recent results in max-plus theory we are able to provide sufficient conditions such that the MPC controller is determined analytically and moreover the stability in terms of Lyapunov and in terms of boundedness of the closed-loop system is guaranteed a priori.     

A low-complexity global approximation-free control scheme with prescribed performance for unknown pure feedback systems

A universal, approximation-free state feedback control scheme is designed for unknown pure feedback systems, capable of guaranteeing, for any initial system condition, output tracking with prescribed performance and bounded closed loop signals. By prescribed performance, it is meant that the output error converges to a predefined arbitrarily small residual set, with convergence rate no less than a certain prespecified value, having maximum overshoot less than a preassigned level. The proposed state feedback controller isolates the aforementioned output performance characteristics from control gains selection and exhibits strong robustness against model uncertainties, while completely avoiding the explosion of complexity issue raised by backstepping-like approaches that are typically employed to the control of pure feedback systems. In this respect, a low complexity design is achieved. Moreover, the controllability assumptions reported in the relevant literature are further relaxed, thus enlarging the class of pure feedback systems that can be considered. Finally, simulation studies clarify and verify the approach.     

Adaptive unit vector control of multivariable systems using monitoring functions

An adaptive sliding‐mode unit vector control approach based on monitoring functions to deal with disturbances of unknown bounds is proposed. An uncertain multivariable linear system is considered with a quite general class of nonsmooth disturbances. Global stabilization/tracking is demonstrated using either state or output feedback. The proposed adaptation method makes the control gain less conservative, becoming large enough when the disturbance grows and becoming smaller when it decreases, leading to reduced chattering effects. In contrast to previous methods, the new switching scheme is able to guarantee a prespecified transient time, maximum overshoot, and steady‐state error for multivariable uncertain plants. The proposed technique is applied to the trajectory tracking control of a surface vessel subjected to ocean currents, wind, and waves. Simulations are presented to show the performance of the new adaptation scheme in this adverse scenario of possibly growing, temporarily large, or vanishing exogenous disturbances.     

Reduced-basis output bounds for approximately parametrized elliptic coercive partial differential equations

We present a technique for the rapid and reliable prediction of linear-functional outputs of elliptic coercive partial differential equations with (approximately) affine parameter dependence. The essential components are (i) (provably) rapidly convergent global reduced-basis approximations – Galerkin projection onto a space W_N spanned by solutions of the governing partial differential equation at N selected points in parameter space; (ii) a posteriori error estimation – relaxations of the error-residual equation that provide inexpensive yet sharp bounds for the error in the outputs of interest; and (iii) off-line/on-line computational procedures – methods which decouple the generation and projection stages of the approximation process. The operation count for the on-line stage – in which, given a new parameter value, we calculate the output of interest and associated error bound – depends only on N, typically very small, and the (approximate) parametric complexity of the problem; the method is thus ideally suited for the repeated and rapid evaluations required in the context of parameter estimation, design, optimization, and real-time control.In our earlier work, we develop a rigorous a posteriori error bound framework for the case in which the parametrization of the partial differential equation is exact; in this paper, we address the situation in which our mathematical model is not complete. In particular, we permit error in the data that define our partial differential operator: this error may be introduced, for example, by imperfect specification, measurement, calculation, or parametric expansion of a coefficient function. We develop both accurate predictions for the outputs of interest and associated rigorous a posteriori error bounds; and the latter incorporate both numerical discretization and model truncation effects. Numerical results are presented for a particular instantiation in which the model error originates in the (approximately) prescribed velocity field associated with a three-dimensional convection-diffusion problem.     

Tracking control of nonlinear systems with improved performance via transformational approach

In this work, we present a transformation‐based adaptive control design, for uncertain strict‐feedback nonlinear systems, to achieve given performance specifications in terms of convergence rate/time, overshoot, steady‐state (zero‐error) precision, in addition to the primary stability requirement. For the case with no uncertainty and known control coefficient, by introducing a time‐varying scaling function and an error‐dependent transformation, we develop a control strategy that is able to achieve exponential and uniform convergence of the tracking error and at the same time maintain the output tracking overshoot to be as small as desired without the need for trajectory initialization resetting. For the case with nonparametric uncertainties and unknown control directions, by employing an additional time‐varying scaling function together with a self‐tuning Nussbaum function, we develop a control scheme that not only secures asymptotic tracking but also guarantees finite time transient process in that the tracking error, prior to converging to zero, is regulated into a prespecified residual set within a prescribed time. Both theoretical analysis and numerical simulations verify the effectiveness and benefits of the proposed method.     

Adaptive neural control of nonlinear MIMO systems with unknown time delays

In this paper, a novel adaptive NN control scheme is proposed for a class of uncertain multi-input and multi-output (MIMO) nonlinear time-delay systems. RBF NNs are used to tackle unknown nonlinear functions, then the adaptive NN tracking controller is constructed by combining Lyapunov-Krasovskii functionals and the dynamic surface control (DSC) technique along with the minimal-learning-parameters (MLP) algorithm. The proposed controller guarantees uniform ultimate boundedness (UUB) of all the signals in the closed-loop system, while the tracking error converges to a small neighborhood of the origin. An advantage of the proposed control scheme lies in that the number of adaptive parameters for each subsystem is reduced to one, triple problems of “explosion of complexity”, “curse of dimension” and “controller singularity” are solved, respectively. Finally, a numerical simulation is presented to demonstrate the effectiveness and performance of the proposed scheme.     

Discontinuous feedback stabilization of minimum-phase semilinear infinite-dimensional systems with application to chemical tubular reactor

This paper develops discontinuous control methods for minimum-phase semilinear infinite-dimensional systems driven in a Hilbert space. The control algorithms presented ensure asymptotic stability, global or local accordingly, as state feedback or output feedback is available, as well as robustness of the closed-loop system against external disturbances with the a priori known norm bounds. The theory is applied to stabilization of chemical processes around prespecified steady-state temperature and concentration profiles corresponding to a desired coolant temperature. Two specific cases, a plug flow reactor and an axial dispersion reactor, governed by hyperbolic and parabolic partial differential equations of first and second order, respectively, are under consideration. To achieve a regional temperature feedback stabilization around the desired profiles, with the region of attraction, containing a prescribed set of interest, a component concentration observer is constructed and included into the closed-loop system so that there is no need for measuring the process component concentration which is normally unavailable in practice. Performance issues of the discontinuous feedback design are illustrated in a simulation study of the plug flow reactor.