State feedback synthesis for on-line optimization of batch reactors with multiple manipulated inputs

On-line optimization of batch reactors with two manipulated inputs

This work develops a numerical algorithm for the calculation of an optimal nonlinear state feedback law for nonlinear systems. A quadratic performance index is used which contains quadratic error terms, and quadratic input penalty terms. The optimization problem is solved using the Hamilton-Jacobi equations, which determine the optimal nonlinear state feedback law. A Newton-Kantorovich iteration is developed for the solution of the pertinent Hamilton-Jacobi equations, which involves solving a Zubov partial differential equation, at each step of the iteration, using a power series method. At step N of the iteration, the method generates the (N + 1)-th order truncation of the Taylor series expansion of the optimal state feedback function. The method is applied to the problem of controlling a system of two non-isothermal continuous stirred tank reactors (CSTR), where an exothermic reaction takes place

Swing-up and stabilization of inverted pendulum by nonlinear optimal state feedback law

Based on the feedback linearization theory of differential geometry theory and the state-space-averaging model of Buck converter working on continuous conduction mode (CCM), the nonlinear state feedback law is proposed. Further, a linear quadratic performance index is presented based on the passivity-based control theory. The state feedback coefficients are optimized using the optimal control theory. The controller is robust to the load variation and variety of parameters. Key waveforms based on simulated extensive work show that the control system has good static and dynamic performance.

Stabilization of a CSTR with two arbitrarily switching modes using modal state feedback linearization

This paper presents a method for designing nonlinear state feedback laws for systems with input and state constraints. The objective is to achieve practical stabilization with large stability region and strong disturbance rejection. Two invariant sets will be constructed within the state constraints: the outer one for stabilization and the inner one for asymptotic disturbance rejection. The nonlinear feedback law is designed such that all trajectories starting from the outer invariant set will enter the inner invariant set and stay there. Both invariant sets will be constructed by using the convex hull function, a recently introduced non-quadratic Lyapunov function. Since the invariant sets are convex hull of ellipsoids, they are able to incorporate the input and state constraints more effectively than simple ellipsoids, thus promising larger stability region within state constraint and stronger disturbance rejection capability. Since the convex hull functions are constructed from quadratic functions, the optimization problems can be treated with LMI-based method. Numerical examples demonstrate the effectiveness of the design methods.

The authors provide an alternative solution to the problem of semiglobal stabilization of a class of minimum phase nonlinear systems that was considered by A.R. Teel (1991). The method used yields a stabilizing linear state feedback law in contrast to a nonlinear state feedback law proposed by Teel. The peaking phenomenon is eliminated by inducing a specific time-scale structure in the linear part of the closed-loop system. This structure consists of a very slow and a very fast time scale. The crucial component in the method is the relation between the slow and the fast time-scales. The proposed linear state feedback control law has a single tunable gain parameter that allows for local asymptotic stability and regulation to the origin for any initial condition in some a priori given (arbitrarily large) bounded set. >

The problem of reinforcement learning (RL) in an unknown nonlinear dynamical system is equivalent to the search for an optimal feedback law utilizing only data from the simulations/rollouts of the dynamical system. Most RL techniques search over a complex global nonlinear feedback parametrization making them suffer from high training times as well as variance. Instead, we advocate searching over a local feedback representation consisting of an open-loop sequence, and an associated optimal linear feedback law completely determined by the open-loop. We show that this alternate approach results in highly efficient training, the answers obtained are globally optimum, repeatable with negligible variance, and hence reliable, and the resulting closed performance is superior to global state-of-the-art RL techniques. Finally, if we replan, whenever required, which is feasible due to the fast and reliable local solution, it allows us to recover the optimal global feedback law.

Composite nonlinear control with state and measurement feedback for general multivariable systems with input saturation

On global external stochastic stabilization of linear systems with input saturation

A unified approach to deadbeat systems design

Concerning the robust model predictive control (MPC) for constrained systems with polytopic model characterization, some approaches have already been given in the literature. One famous approach is an off-line MPC, which off-line finds a state-feedback law sequence with corresponding ellipsoidal domains of attraction. Originally, each law in the sequence was calculated by fixing the infinite horizon control moves as a single state feedback law. This paper optimizes the feedback law in the larger ellipsoid, foreseeing that, if it is applied at the current instant, then better feedback laws in the smaller ellipsoids will be applied at the following time. In this way, the new approach achieves a larger domain of attraction and better control performance. A simulation example shows the effectiveness of the new technique.

In this paper, we show that a linear discrete-time system subject to input saturation is semi-globally exponentially stabilizable via linear state and/or output feedback laws as long as the system in the absence of input saturation is stabilizable and detectable, and has all its poles located inside or on the unit circle. Furthermore, the semi-globally stabilizing feedback laws are explicitly constructed. The results presented here are parallel to our earlier results on the continuous-time counterpart (1993).

We consider the robust and perfect tracking (RPT) problem for multivariable linear systems with external disturbances. The problem is to design a proper controller such that the resulting overall closed-loop system is asymptotically stable and the controlled output almost perfectly tracks a given reference signal with an arbitrarily fast settling time in the face of external disturbances and initial conditions. We derive a set of necessary and sufficient conditions under which the RPT problem is solvable. Under these solvability conditions, we develop algorithms for constructing state and output feedback laws, explicitly parameterized in /spl epsi/, that solve the RPT problem. In our construction of feedback laws, we propose a controller structure which enables us to design a tracking controller without introducing additional integrators regardless what type the system is.

Global asymptotic stabilization of nominally linear uncertain systems is considered where uncertain elements in the plant are modelled as cone bounded nonlinearities. At first, a linear time-invariant state feedback law ensuring global aymptotic closed-loop stability is obtained. The algorithm which calculates such a feedback law is simple and straightforward. It does not involve repeated solutions of a parameter dependent algebraic Riccati or any such nonlinear equations. Any state feedback law thus developed can then be implemented via an observer specially designed to preserve the global asymptotic stability of the closed-loop system.