Suboptimal control of nonlinear systems

The Modified LJ search method used by Nair[1] to find suboptimal controllers for linear systems is extended to the case of nonlinear systems. To illustrate the method, three numerical examples are discussed.     

Reliable control of nonlinear systems

In this paper, we extend Veillette's results (1995) to the study of reliable linear-quadratic regulator problem for nonlinear systems. This is achieved by employing the Hamilton-Jacobi inequality in the nonlinear case instead of algebraic Riccati equation in the linear one. The proposed state-feedback controllers are shown to be able to tolerate the outage of actuators within a prespecified subset of actuators. Both the gain margins of guaranteeing system stability and retaining a performance bound are estimated     

Feedback control of nonlinear systems

This paper deals with the design of (memoryless) state-feedback laws for systems modelled by nonlinear differential equations which are affine in the inputs. The purpose of the design is to obtain a (locally) internally stable closed-loop system in which the effect of exogenous inputs on a prescribed error (or, more in general, on a penalty variable) is attenuated. Two standard setups are considered: in the first one, the ratio between the energy associated with the penalty variable and that associated with the exogenous input is required to be bounded by a constant 0 < γ this setup includes (to some extent) the standard H_∞ control problem of linear system theory. In the second one, the penalty variable is required to converge to 0 as t ∞; this setup generalizes the so-called servomechanism problem of linear system theory.     

Adaptive control of nonlinear systems with nonlinear parameterization

An adaptive feedback regulation scheme is proposed for a class of single input nonlinear systems, with nonlinear parameterizations. A proof of local regulation is given. The results are validated through a simulation study.     

Suboptimal terminal feedback control of nonstationary, nonlinear systems

An adaptive approach for terminal feedback control of nonlinear systems with time-varying parameters is presented. Viability of the approach is established with simultation results and comparisons to existing approaches.     

Receding horizon control of nonlinear systems

The receding horizon control strategy provides a relatively simple method for determining feedback control for linear or nonlinear systems. The method is especially useful for the control of slow nonlinear systems, such as chemical batch processes, where it is possible to solve, sequentially, open-loop fixed-horizon, optimal control problems online. The method has been shown to yield a stable closed-loop system when applied to time-invariant or time-varying linear systems. It is shown that the method also yields a stable closed-loop system when applied to nonlinear systems     

Adaptive linear control of nonlinear systems

The theory of stable parameter adaptive control has advanced to allow linear time-varying plants. However, a more honest view of such systems is that they are often derived from inexact linearization about a trajectory of a nonlinear system. Standard adaptive control based on a linear model can then be interpreted as one way to realize a nonlinear controller for a nonlinear plant. The implications of this view are studied. Analytically, the stability problem is seen to be equivalent to showing robustness to time-varying parameters and a locally bounded model uncertainty. It is shown that if the trajectory is known to be within a bound, a parameter estimator with projection can ensure boundedness of departures from the trajectory     

Feedback affinization of nonlinear control systems

In this paper conditions for the nonlinear control system

to have a nonlinear feedback control

u=(x,v), vΩ′R^m′, m′m, 0Ω′

such that the nonlinear system takes a form of an affine system

are presented. All results require algebraic operations and differentiation of functions only.     

Controllability of nonlinear stochastic control systems

In the paper sufficient conditions for ‘deterministic weak controllability’ of nonlinear Itô equations of the form are given.     

Invertibility of multivariable nonlinear control systems

This paper gives sufficient conditions for the invertibility of nonlinear control systems of the formdot{x}= A(x)+ u_{1}B_{1}(x) +... + u_{m} B_{m}(x);y=c(x), where the state space is a real analytic manifold. These conditions are also necessary in the case of single-input nonlinear systems and multivariable time-invariant linear systems. For invertible systems we construct nonlinear inverse systems.     

Unconstrained receding-horizon control of nonlinear systems

It is well known that unconstrained infinite-horizon optimal control may be used to construct a stabilizing controller for a nonlinear system. We show that similar stabilization results may be achieved using unconstrained finite horizon optimal control. The key idea is to approximate the tail of the infinite horizon cost-to-go using, as terminal cost, an appropriate control Lyapunov function. Roughly speaking, the terminal control Lyapunov function (CLF) should provide an (incremental) upper bound on the cost. In this fashion, important stability characteristics may be retained without the use of terminal constraints such as those employed by a number of other researchers. The absence of constraints allows a significant speedup in computation. Furthermore, it is shown that in order to guarantee stability, it suffices to satisfy an improvement property, thereby relaxing the requirement that truly optimal trajectories be found. We provide a complete analysis of the stability and region of attraction/operation properties of receding horizon control strategies that utilize finite horizon approximations in the proposed class. It is shown that the guaranteed region of operation contains that of the CLF controller and may be made as large as desired by increasing the optimization horizon (restricted, of course, to the infinite horizon domain). Moreover, it is easily seen that both CLF and infinite-horizon optimal control approaches are limiting cases of our receding horizon strategy. The key results are illustrated using a familiar example, the inverted pendulum, where significant improvements in guaranteed region of operation and cost are noted     

Approximate linearization of nonlinear control systems

The paper address the problem of approximate linearization of a nonlinear control system by state feedback or dynamic feedback. The main result proved is that if the fast k d-relative degrees are equal to each other, then the input-output response of a nonlinear control system can be linearized to degree k. Any system having linear d-relative degree can be linearized to any degree by dynamic feedbacks. One example of signal tracking using dynamic feedback linearization method to improve the performance is also given.     

Feedback decomposition of nonlinear control systems

By using the recently developed (differential) geometric approach to nonlinear systems, a feedback decomposition for nonlinear control systems is derived.     

非线性系统输出反馈控制

本文针对一般非线性系统,构造了迭代学习观测器,基于该迭代学习观测器的状态和可调参数设计了输出反馈控制律,通过选择可调参数自适应调节律的适当形式,保证了整个系统的渐近稳定性和输出反馈控制律的有界性。计算机模拟显示所提出方法的有效性。     

Constrained tracking control of nonlinear systems

The problem of tracking control for nonlinear systems subject to bounded-control constraints is considered. A novel nonlinear, continuous-time, predictive control approach is taken. Control laws are obtained for both nonlinear systems that are affine in the control and general nonlinear systems. Efficient and reliable algorithms based on contraction mapping theorems are devised for on-line implementation. Illustrative examples are provided.     

Extremum-seeking control of state-constrained nonlinear systems

An extremum-seeking control problem is posed for a class of nonlinear systems with unknown dynamical parameters, whose states are subject to convex, pointwise inequality constraints. Using a barrier function approach, an adaptive method is proposed for generating setpoints online which converge to the feasible minimizer of a convex objective function containing the unknown dynamic parameters. A tracking controller regulates system states to the generated setpoint via state feedback, while maintaining feasibility of the state constraints. A simulation example demonstrates application of the method.