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Optimal Control by Polynomial Approximation: The Discrete Time Case
IFAC Proceedings Volumes, 1989Abstract This paper discusses optimal control of discrete time nonlinear systems. All of the functions discussed are assumed to be analytic. Each function is expanded in a Taylor series. By parameterizing the series using tensor algebraic techniques, explicit expressions for the terms in the series expansion for the feedback controller are obtained ...
J.A. O'Sullivan, M.K. Sain
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Approximations for discrete-time adaptive control: Construction of ε-optimal controls
Mathematics of Control, Signals, and Systems, 1991The following problem of stochastic optimal control is considered. To minimize the functional \(G(u)=M\left\{\sum^{N-1}_{n=0}g_ 1(x_ n,u_ n)+g_ 2(x_ N)\right\}\to\inf\) under the conditions \[ x_{n+1}=f_ 1(x_ n,u_ n)+\theta f_ 2(x_ n,u_ n)+\sigma(x_ n,u_ n)w_{n+1},\qquad n=0,\dots,N-1, \] where \(x_ 0\) is the initial condition with density of ...
Wolfgang J. Runggaldier, Omar Zane
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Discrete approximation of relaxed optimal control problems
Journal of Optimization Theory and Applications, 1990We consider a general nonlinear optimal control problem for systems governed by ordinary differential equations with terminal state constraints. No convexity assumptions are made. The problem, in its so- called relaxed form, is discretized and necessary conditions for discrete relaxed optimality are derived. We then prove that discrete optimality [resp.
Chryssoverghi, I., Bacopoulos, A.
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Discrete Approximations to Continuous Optimal Control Problems
SIAM Journal on Control, 1969It is demonstrated that if P is a continuous optimal control problem whose system of differential equations is linear in the control and the state variables, and whose control and state variable constraint sets are convex, a direct method of determining an optimal solution of P exists. It is demonstrated that such a “continuous” problem can be replaced
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Regularity Properties of Optimal Controls with Application to Discrete Approximation
Journal of Optimization Theory and Applications, 1999The paper is an improvement of the recent result of \textit{A. L. Dontchev} [SIAM J. Control Optimization 34, No. 4, 1315-1328 (1996; Zbl 0851.49023)] about discrete approximations under uniform coercivity conditions on the discrete solutions for differential equations. Moreover, the regularity is further specified by Lipschitz continuity. The form of \
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An approximate optimal control for discrete models: Its design
Automation and Remote Control, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Approximate optimal control of discrete I/O systems with C/GMRES
2015 European Control Conference (ECC), 2015This paper proposes an optimal control approach to control systems described by discrete time I/O models. In particular, the C/GMRES method, which is a curse-of-dimensionality free and fast approximative optimal control method is adapted to this purpose.
J. Blumenschein +5 more
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A hybrid approximation scheme for discretizing constrained quadratic optimal control problems
Journal of the Franklin Institute, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hamid Reza Marzban +1 more
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Applied Optics, 2014
Since the discovery of materials with negative refractive index, widely known as metamaterials, it has been possible to develop new devices that utilize a metamaterial's ability to control the path of electromagnetic energy. Of particular promise, and already under intensive development for commercial applications, are metamaterial antennas for ...
Mikala, Johnson +3 more
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Since the discovery of materials with negative refractive index, widely known as metamaterials, it has been possible to develop new devices that utilize a metamaterial's ability to control the path of electromagnetic energy. Of particular promise, and already under intensive development for commercial applications, are metamaterial antennas for ...
Mikala, Johnson +3 more
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Successive approximation approach of optimal control for nonlinear discrete-time systems
International Journal of Systems Science, 2005A successive approximation approach designing optimal controller is developed for affine non-linear discrete-time systems with a quadratic performance index. By using this approach the original optimal control problem is transformed into a sequence of nonhomogeneous linear two-point boundary value (TPBV) problems. The optimal control law consists of an
G.-Y. Tang, H.-H. Wang
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