Optimal Finite-Time Feedback Controllers for Nonlinear Systems with Terminal Constraints

Vadali, Srinivas R.; Sharma, Rajnish

doi:10.2514/1.16790

Cited by 33 publications

(30 citation statements)

References 19 publications

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“…The terminal constraints in the problem definition are associated with terminal Lagrange multipliers, , that are constant over time. The relationship between the costate vector t and the gradient of the value function that connects dynamic programming and the calculus of variation approaches is: t @I xt; t @xt (5) A key relationship between the terminal Lagrange multipliers and optimal return function is established in [21] @I xt; t @ 0 xt f f (6) The SSM is a procedure to approximately solve the HJB equation. The method is thoroughly discussed in [21] and consequently only highlights are presented here.…”

Section: Brief Overview Of the Series Solution Methodsmentioning

confidence: 99%

“…Conversely, a recently developed series solution method has been shown to be useful for problems subject to nonlinear terminal constraints. Vadali and Sharma [21] recently presented a series solution method (SSM) to synthesize nonlinear feedback solutions to finite time, nonlinear optimal control problems subject to nonlinear terminal constraints. The SSM can be considered a generalization of the well-known sweep method that is tailored to handle nonlinear polynomial systems with nonlinear terminal constraints.…”

Section: Introductionmentioning

confidence: 99%

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Optimal Nonlinear Feedback Control Design Using a Waypoint Method

Sharma

Vadali

Hurtado

2011

Journal of Guidance, Control, and Dynamics

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This paper discusses an innovative idea of blending the notion of a waypoint scheme with a series solution method developed by the authors for solving the Hamilton-Jacobi-Bellman equation in the context of designing optimal feedback control laws for nonlinear dynamic systems subject to terminal constraints. The overall time interval of the given problem is partitioned into smaller segments, and the series solution method is applied within each segment using stored gains that are computed from one segment only. The methodology is applied to highly nonlinear systems including a minimum orbit transfer problem. Several examples are demonstrated, and the results are compared with the corresponding open-loop solutions to demonstrate the efficacy of the proposed method.

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Section: Brief Overview Of the Series Solution Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimal Nonlinear Feedback Control Design Using a Waypoint Method

Sharma

Vadali

Hurtado

2011

Journal of Guidance, Control, and Dynamics

Self Cite

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“…First, due to the time-varying HJB equation, the solution to the HJB equation for a finite-horizon optimal control [14][15][16] is timevarying in nature, which complicates the analysis compared to the infinite horizon optimal control. Second, the value function should satisfy terminal constraint whereas the constrained condition is taken as zero for infinite horizon optimal control.…”

Section: Introductionmentioning

confidence: 99%

“…Second, the value function should satisfy terminal constraint whereas the constrained condition is taken as zero for infinite horizon optimal control. In [15], a method of power series to deal with the finite-horizon optimal problem with small nonlinearities was given, and in [16] the time-varying HJB equation was changed into a state-dependent differential Riccati equation, then an approximate optimal control was obtained by a truncation in the control equation. In [16,17], the neural network with time-dependent weights was utilized and calculated in backward-in-time manner.…”

Section: Introductionmentioning

confidence: 99%

Online finite-horizon optimal learning algorithm for nonzero-sum games with partially unknown dynamics and constrained inputs

et al. 2016

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“…monomial expansions [8,9], orthogonal functions [10], radial basis functions [11], and neural networks [12]. Methods based on monomial expansions minimize local approximation errors and are best suited for systems with polynomial nonlinearities.…”

Section: Introductionmentioning

confidence: 99%

Higher Order Methods for Determining Optimal Controls and Their Sensitivities

McCrate

Vadali

Bhattacharya

2010

AIAA Guidance, Navigation, and Control Conference

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The solution of optimal control problems through the Hamilton-Jacobi-Bellman (HJB) equation offers guaranteed satisfaction of both the necessary and sufficient conditions for optimality. However, finding an exact solution to the HJB equation is a near impossible task for many optimal control problems. This thesis presents an approximation method for solving finite-horizon optimal control problems involving nonlinear dynamical systems. The method uses finite-order approximations of the partial derivatives of the cost-to-go function, and successive higher-order differentiations of the HJB equation. Natural byproducts of the proposed method provide sensitivities of the controls to changes in the initial states, which can be used to approximate the solution to neighboring optimal control problems. For highly nonlinear problems, the method is modified to calculate control sensitivities about a nominal trajectory. In this framework, the method is shown to provide accurate control sensitivities at much lower orders of approximation. Several numerical examples are presented to illustrate both applications of the approximation method.

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Optimal Finite-Time Feedback Controllers for Nonlinear Systems with Terminal Constraints

Cited by 33 publications

References 19 publications

Optimal Nonlinear Feedback Control Design Using a Waypoint Method

Optimal Nonlinear Feedback Control Design Using a Waypoint Method

Online finite-horizon optimal learning algorithm for nonzero-sum games with partially unknown dynamics and constrained inputs

Higher Order Methods for Determining Optimal Controls and Their Sensitivities

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