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

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

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.

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

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

On global external stochastic stabilization of linear systems with input saturation

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.

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

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. >

This article deals with the problem of dissipative control synthesis for a class of descriptor systems with uncertainties in the derivative matrix. Attention is focused on the design of a proportional plus derivative (PD) state feedback, which guarantees that the closed-loop system is robustly stable and strict dissipative. Firstly, a sufficient condition for the closed-loop system is robustly stable and strict dissipative is presented by using a simple idea of changing the problem to the corresponding problem of an augmented uncertain system. Then, a PD controller is constructed by solving LMIs. Finally, a numerical example is given to demonstrate that the proposed method is effective.

This paper is concerned with the nonlinear static state feedback stabilization of time-invariant linear multivariable continuous-time systems with friction driven backlash in the control inputs. A time-invariant static nonlinear state feedback compensator is proposed, easily obtainable solving an algebraic Riccati equation. The global asymptotic stability of the resulting closed-loop nonlinear system is proved using the Lyapunov's direct method and the La Salle's invariance principle. A simulation study shows that the proposed nonlinear state feedback compensator achieves an overall stabilization performance significantly better than the known backlash inverse compensator.

The paper is concerned with a problem of adaptive tracking system control synthesis. It is assumed that a nonlinear object dynamics (model structure) is (partially) unknown and some of its nonlinear characteristics can be approximated by a sort of functional approximators. It has been proven that a nonlinear state feedback plus parameter adaptation are able to ensure its asymptotic stability. The proposed controller design is based on modified adaptive backstepping method. In this approach, as opposite to the standard backstepping, the design process has been reduced to a single iteration, which enables avoiding complicated recursive procedure. An extra task here is to find a control synthesis of linear-like, chained system. The solution of the last problem in general framework is also presented. The obtained thereby controller has several attractive features of both the feedback linearization and backstepping schemes.

This paper presents a nonlinear control design method for robust stabilization and robust performance of linear differential inclusions. A recently introduced non-quadratic Lyapunov function, the convex hull quadratic function, is used for the construction of nonlinear state feedback laws. Design objectives include stabilization with maximal convergence rate, disturbance rejection with minimal reachable set and least /spl Lscr//sub 2/ gain. Conditions for stabilization and performances are derived in terms of bilinear matrix inequalities (BMIs), which cover the existing linear matrix inequality (LMI) conditions as special cases. Optimization problems with BMI constraints are formulated and solved effectively by combining the path-following algorithm and the direct iterative algorithm. The design results are guaranteed to be at least as good as the existing results obtained from LMI conditions. In most examples, significant improvements on system performances have been achieved, which demonstrate the advantages of using nonlinear feedback control over linear feedback control for linear differential inclusions. It is also observed through numerical computation that nonlinear control strategies may help to reduce control effort substantially.

This paper considers the control synthesis problem and its solution using symbolic regression. Symbolic regression methods, which were previously called genetic programming methods, allow one to use a computer to find not only the parameters of a given regression function but also its structure. Unlike other works on solving the control synthesis problem using symbolic regression, the novelty of this paper is that for the first time this work employs a training dataset to address the problem of general control synthesis. Initially, the optimal control problem is solved from each point in a given set of initial states, resulting in a collection of control functions expressed as functions of time. A reference model is then integrated into the control object model, which generates optimal motion trajectories using the derived optimal control functions. The control synthesis problem is framed as an approximation task for all optimal trajectories, where the control function is sought as a function of the deviation of the object from the specified terminal state. The optimization criterion for solving the synthesis problem is the accuracy of the object’s movement along the optimal trajectory. The paper includes an example of solving the control synthesis problem for a mobile robot using a supervised machine learning method. A relatively new method of symbolic regression, the method of variational complete binary genetic programming, is studied and proposed for the solution of the control synthesis problem.

A cooperative dynamic hybrid control method for multimotion robotic mechanisms handling a single object whose motion is constrained by environment is discussed. This method takes the manipulator dynamics and object dynamics into consideration and is for controlling the motion of the object as well as for controlling the constraint force and the internal force. The following results are obtained: (1) the force and kinematic relations are established for arms grasping and manipulating an object using various types of end effector; and (2) using the first result, a nonlinear state feedback law for the joint driving force that linearizes and decouples the robot system with respect to the object motion, constraint force, and internal force is given. A basic structure of the dynamic hybrid control system with a servo compensator is presented. The effectiveness of the proposed approach has been examined by a simple experiment. These results are useful for the fine manipulation of an object, in the sense that one can specify the controller characteristics independently for the individual specification of the object motion, the interaction between the object and its environment, and the grasping of the object. >

On-line optimization of batch reactors with two manipulated inputs