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1.
We discuss methods of approximating stable neutral functional differential equations and associated optimal control problems by sequences of optimal control problems for ordinary differential equations. By introducing a class of “mollified” neutral functional differential equations, convergence of the linear interpolating spline and the averaging approximation scheme is proved. A number of numerical examples are included. 相似文献
2.
A numerical algorithm to obtain the consistent conditions satisfied by singular arcs for singular linear–quadratic optimal
control problems is presented. The algorithm is based on the Presymplectic Constraint Algorithm (PCA) by Gotay-Nester (Gotay
et al., J Math Phys 19:2388–2399, 1978; Volckaert and Aeyels 1999) that allows to solve presymplectic Hamiltonian systems and that provides a geometrical framework to the Dirac-Bergmann theory
of constraints for singular Lagrangian systems (Dirac, Can J Math 2:129–148, 1950). The numerical implementation of the algorithm is based on the singular value decomposition that, on each step, allows to
construct a semi-explicit system. Several examples and experiments are discussed, among them a family of arbitrary large singular
LQ systems with index 2 and a family of examples of arbitrary large index, all of them exhibiting stable behaviour.
Research partially supported by MEC grant MTM2004-07090-C03-03. SIMUMAT-CM, UC3M-MTM-05-028 and CCG06-UC3M/ESP-0850. 相似文献
3.
This contribution extends a numerical method for solving optimal control problems by dynamic programming to a class of hybrid dynamic systems with autonomous as well as controlled switching. The value function of the hybrid control system is calculated based on a full discretization of the state and input spaces. A bound for the error due to discretization is obtained from modeling the error as perturbation of the continuous dynamics and the cost terms. It is shown that the bound approaches zero and that the value function of the discretized variant converges to the value function of the original problem if the discretization parameters go to zero. The performance of a numerical scheme exploiting the discretized system is illustrated for two different examples treated previously in literature. 相似文献
5.
In the paper, we consider the bioprocess system optimal control problem. Generally speaking, it is very difficult to solve this problem analytically. To obtain the numerical solution, the problem is transformed into a parameter optimization problem with some variable bounds, which can be efficiently solved using any conventional optimization algorithms, e.g. the improved Broyden–Fletcher–Goldfarb–Shanno algorithm. However, in spite of the improved Broyden–Fletcher–Goldfarb–Shanno algorithm is very efficient for local search, the solution obtained is usually a local extremum for non-convex optimal control problems. In order to escape from the local extremum, we develop a novel stochastic search method. By performing a large amount of numerical experiments, we find that the novel stochastic search method is excellent in exploration, while bad in exploitation. In order to improve the exploitation, we propose a hybrid numerical optimization algorithm to solve the problem based on the novel stochastic search method and the improved Broyden–Fletcher–Goldfarb–Shanno algorithm. Convergence results indicate that any global optimal solution of the approximate problem is also a global optimal solution of the original problem. Finally, two bioprocess system optimal control problems illustrate that the hybrid numerical optimization algorithm proposed by us is low time-consuming and obtains a better cost function value than the existing approaches. 相似文献
6.
Some notions related to approximate solutions and to the approximation of extremum problems for nonlinear infinite-dimensional systems are proposed. Optimization problems for nonlinear parabolic equations with a fixed terminal state and on an infinite time interval, as well as for singular stationary systems with phase constraints, are illustrated by several examples. 相似文献
7.
To determine the optimum in nonlinear optimal control problems, it is proposed to convert the continuous problems into a form suitable for nonlinear programming (NLP). Since the resulting finite-dimensional NLP problems can present multiple local optima, a global optimization approach is developed where random starting conditions are improved by using special line searches. The efficiency, speed, and reliability of the proposed approach is examined by using two examples.Financial support from the Natural Science and Engineering Research Council under Grant A-3515 as well as an Ontario Graduate Scholarship are gratefully acknowledged. All the computations were done with the facilities of the University of Toronto Computer Centre and the Ontario Centre for Large Scale Computations. 相似文献
8.
Optimal control problems for bilinear systems are studied and solved with a view to approximating analogous problems for general nonlinear systems. For a given bilinear optimal control problem, a sequence of linear problems is constructed, and their solutions are shown to converge to the desired solution. Also, the direct solution to the Hamilton-Jacobi equation is analyzed. A power-series approach is presented which requires offline calculations as in the linear case (Riccati equation). The methods are compared and illustrated. Relations to classical linear systems theory are discussed. 相似文献
9.
Existence theorems are stated and proved for optimal control problems monitored by a nonlinear Volterra-type integral equation. Growth conditions are taken into consideration which ensure the needed compactness on the set of trajectories and entail the existence of the usual optimal solutions for the given problem. Weak or approximate solutions are taken into consideration in a subsequent paper.The author would like to express his appreciation to Professor L. Cesari and Professor M. B. Suryanarayana for many helpful conversations and suggestions for the improvement of earlier versions of this paper. 相似文献
10.
Summary In this paper we study optimal control problems for infinite dimensional systems governed by a semilinear evolution equation. First under appropriate convexity and growth conditions, we establish the existence of optimal pairs. Then we drop the convexity hypothesis and we pass to a larger system known as the « relaxed system ». We show that this system has a solution and the value of the relaxed optimization problem is equal to the value of the original one. Next we restrict our attention to linear systems and establish two « bang-bang » type theorems. Finally we present some examples from systems governed by partial differential equations.Research supported by N.S.F. Grant-8602313.Work done while on leave at the « University of Thessaloniki, School of Technology, Mathematics Division, Thessaloniki 54006, Greece ». 相似文献
11.
We study the problem of the existence of the optimal control of monotone nonlinear distributed systems with generalized interaction.
The method proosed allows one to study monotone nonlinear systems with point, impulse, point impulse, and nonstationary controls
as well as with their generalizations. Bibliography: 2 titles.
Translated from Obcyslyuval'na ta Prykladna Matematyka,, No. 81, 1997, pp 60–61 相似文献
12.
Power-series methods are developed for designing approximately optimal state regulators for a nonlinear system subject to white Gaussian random disturbances. The performance index of the control is an ensemble average of a quadratic form. A perfect observation of the system state is assumed. When the system nonlinearity is small and it is characterized by a polynomial function of the state, a definite method is presented to construct a suboptimal feedback control of a power-series form in a small nonlinearity parameter. If the variance of noise is small, an alternative method is also applicable which yields a suboptimal control in a power series with respect to a variance parameter. A simple one-dimensional problem is examined to make comparison between controls of the two different forms. 相似文献
13.
We consider a family of nonlinear optimal control problems depending on a parameter. Under the assumption of a second-order sufficient optimality condition it is shown that the solutions of the problems as well as the associated Lagrange multipliers are Lipschitz continuous functions of the parameter. 相似文献
14.
The optimal tracking control (OTC) problem for a class of affine nonlinear composite systems with similar structure is considered. By using a modeling technique, the nonlinear similar composite system is first transformed into some quasi-decoupled subsystems. Then the high-order, strongly coupled, nonlinear two-point boundary value (TPBV) problem is transformed into a sequence of linear decoupled TPBV problems through a successive approximation procedure. The obtained OTC law consists of an accurate linear term and a nonlinear compensation term which is the limit of the adjoint vector sequence. A suboptimal tracking control law is obtained by truncating a finite iterative result of the adjoint vector sequence as its nonlinear compensation term. 相似文献
15.
A neural network hybrid adaptive control framework for nonlinear uncertain hybrid dynamical systems is developed. The proposed hybrid adaptive control framework is Lyapunov-based and guarantees partial asymptotic stability of the closed-loop hybrid system; that is, asymptotic stability with respect to part of the closed-loop system states associated with the hybrid plant states. A numerical example is provided to demonstrate the efficacy of the proposed hybrid adaptive stabilization approach. 相似文献
16.
A novel state-space self-tuning control methodology for a nonlinear stochastic hybrid system with stochastic noise/disturbances is proposed in this paper. via the optimal linearization approach, an adjustable NARMAX-based noise model with estimated states can be constructed for the state-space self-tuning control in nonlinear continuous-time stochastic systems. Then, a corresponding adaptive digital control scheme is proposed for continuous-time multivariable nonlinear stochastic systems, which have unknown system parameters, measurement noise/external disturbances, and inaccessible system states. The proposed method enables the development of a digitally implementable advanced control algorithm for nonlinear stochastic hybrid systems. 相似文献
17.
The paper deals with model predictive control (MPC) of nonlinear hybrid systems with discrete inputs based on reachability analysis. In order to implement a MPC algorithm, a model of the process that we are dealing with is needed. In the paper, a hybrid fuzzy modelling approach is proposed. The hybrid system hierarchy is explained and the Takagi–Sugeno fuzzy formulation for hybrid fuzzy modelling purposes is tackled. An efficient method of identification of the hybrid fuzzy model is also discussed. An algorithm that is–due to its MPC nature–suitable for controlling a wide spectrum of systems (provided that they have discrete inputs only) is presented. The benefits of the algorithm employing a hybrid fuzzy model are verified on a batch reactor example. The results suggest that by suitably determining the cost function, satisfactory control can be attained, even when dealing with complex hybrid–nonlinear–stiff systems such as the batch reactor. Finally, a comparison between MPC employing a hybrid linear model and a hybrid fuzzy model is carried out. It has been established that the latter approach clearly outperforms the approach where a linear model is used. 相似文献
18.
The aim of this paper is to present a stochastic maximum principle for an optimal control problem of switching systems. It presents necessary conditions of optimality in the form of a maximum principle for stochastic switching systems, in which the dynamic of the constituent processes takes the form of stochastic differential equations. The restrictions on transitions for the system are described through equality constraints. 相似文献
19.
A numerical approach to design control invariant sets for constrained nonlinear discrete-time systems with guaranteed optimality
is proposed in this paper. The addressed approach is based on the fact that zonotopes are more flexible for representing sets
than boxes in interval analysis. Then the solver of set inversion via interval analysis is extended to set inversion via zonotope
geometry by introducing the novel idea of bisecting zonotopes. The main feature of the extended solver of set inversion is
the bisection and the evolution of a zonotope rather than a box. Thus the shape of admissible domains for set inversion can
be broadened from boxes to zonotopes and the wrapping effect can be reduced as well by using the zonotope evolution instead
of the interval evolution. Combined with global optimization via interval analysis, the extended solver of set inversion via
zonotope geometry is further applied to design control invariant sets for constrained nonlinear discrete-time systems in a
numerical way. Finally, the numerical design of a control invariant set and its application to the terminal control of the
dual-mode model predictive control are fulfilled on a benchmark Continuous-Stirred Tank Reactor example. 相似文献
20.
The problem of fault identification in hybrid systems is investigated. It is assumed that the hybrid systems under consideration consist of a finite automaton, the set of nonlinear differential equations, and so-called mode activator that coordinates the action of these two parts. To solve the fault identification problem, sliding mode observers are used. The suggested approach for constructing sliding mode observers is based on the reduced order model of the original system. This allows to reduce complexity of sliding mode observers and relax the limitations imposed on the original system. Examples illustrate details of the solution. 相似文献
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