Suboptimal Control Of Nonlinear Systems Research Articles

Closed-form solution to finite-horizon suboptimal control of nonlinear systems

Finite-horizon optimal control of input-affine nonlinear systems with fixed final time is considered in this study. It is first shown that the associated Hamilton–Jacobi–Bellman partial differential equation to the problem is reducible to a state-dependent differential Riccati equation after some approximations. With a truncation in the control equation, a near optimal solution to the problem is obtained, and the global onvergence properties of the closed-loop system are analyzed. Afterwards, an approximate method, called Finite-horizon State-Dependent Riccati Equation (Finite-SDRE), is suggested for solving the differential Riccati equation, which renders the origin a locally exponentially stable point. The proposed method provides online feedback solution for controlling different initial conditions. Finally, through some examples, the performance of the resulting controller in finite-horizon control is analyzed. Copyright © 2014 John Wiley & Sons, Ltd.

Robust suboptimal control of nonlinear systems

In this paper, we consider a nonlinear dynamic system with uncertain parameters. Our goal is to choose a control function for this system that balances two competing objectives: (i) the system should operate efficiently; and (ii) the system’s performance should be robust with respect to changes in the uncertain parameters. With this in mind, we introduce an optimal control problem with a cost function penalizing both the system cost (a function of the final state reached by the system) and the system sensitivity (the derivative of the system cost with respect to the uncertain parameters). We then show that the system sensitivity can be computed by solving an auxiliary initial value problem. This result allows one to convert the optimal control problem into a standard Mayer problem, which can be solved directly using conventional techniques. We illustrate this approach by solving two example problems using the software MISER3.

A Suboptimal Controller Design Methodology for Input-Output Feedback-Linearizable Systems

This paper addresses suboptimal control of nonlinear systems which can be feedback-linearized from input to output. The case of input-to-state linearizable systems is also covered as a special case. The method is thus applicable to all nonlinear systems which can be partially linearized using the method of output-feedback linearization while having a stable internal (or zero) dynamics. The well-known LQR technique applied to the linearized system does not guarantee the suboptimality of the nonlinear system. This paper uses output feedback linearization technique to partially linearize the system and then designs an output-feedback for the feedback-linearized system in such a way that it ensures suboptimal performance of the original nonlinear system. The proposed method can optimize any arbitrary smooth function of states and input. The proposed controller is, however, suboptimal due to the facts that (1) the form of the controller is a linear static feedback of the linearized state, (2) the search algorithm may fall into a local extremum rather than a global, and (3) the calculated controller depends on the initial conditions. The method is successfully applied to control design of the longitudinal subsystem of a laboratory double-rotor helicopter and the results are discussed and compared with those of the LQR method.

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.

Use of piecewise linearization for suboptimal control of non-linear systems†

This paper develops the theory for solving piecewise-linear optimal control problems and then employs this theory to obtain suboptimal solutions for controlling non-linear systems. The non-linear system is first approximated by a piecewise-linear model. A jump condition on the adjoint variables and a continuity condition on the Hamiltonian are derived and utilized to obtain the optimal solution to the piecewise-linear model. This control is then considered as a suboptimal solution to the non-linear problem. The piecewise-linear modelling technique provides a means of decoupling the system and adjoint equations and hence provides a simple means of calculating the suboptimal control. A variable mass, minimum-energy problem is solved to illustrate the technique. A feedback scheme is introduced to minimize the boundary and cost errors.

Suboptimal control of nonlinear systems: I. Unconstrained

AbstractAn algorithm for suboptimal control of nonlinear unconstrained systems is developed. The result is closed loop, uses the familiar linear‐quadratic optimal approach, and minimizes computational time and effort. Numerous examples are presented.

Suboptimal control of nonlinear systems: II. Constrained

AbstractThe previous development in suboptimal control of nonlinear unconstrained systems is extended to constrained systems by the use of penalty functions in an augmented sense. This converts the constrained control problem into an unconstrained one with all of the advantages previously discussed. Numerical examples are presented.