Optimal Control

Lewis, Frank L.; Vrabie, Draguna; Syrmos, V.L.

doi:10.1002/9781118122631

Cited by 1,818 publications

(1,236 citation statements)

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“…which holds due to Bellman's principle of optimality (see [29], Chapter 6). As the minimization is performed, the optimal control policy is also formed as µk pζq " arg min…”

Section: Control Objective and Dynamic Programming Solutionmentioning

confidence: 99%

“…In particular, the UAV was simulated using the high fidelity flight simulator Aviones while the target trajectory was that encountered during the flight test for the stochastic optimal control policy. The wind field estimate of the simulated autopilot was utilized in (28) and (29) to accommodate nonzero winds with the original control policies. Moreover, we conducted multiple 15-minute experiments to test each policy's performance for various constantspeed winds.…”

Section: Wind Considerationsmentioning

confidence: 99%

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Vision-based target tracking with a small UAV: Optimization-based control strategies

Quintero

Hespanha

2014

Control Engineering Practice

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This paper considers the problem of a small, fixed-wing UAV equipped with a gimbaled camera autonomously tracking an unpredictable moving ground vehicle. Thus, the UAV must maintain close proximity to the ground target and simultaneously keep the target in its camera's visibility region. To achieve this objective robustly, two novel optimizationbased control strategies are developed. The first assumes an evasive target motion while the second assumes a stochastic target motion. The resulting optimal control policies have been successfully flight tested, thereby demonstrating the efficacy of both approaches in a real-world implementation and highlighting the advantages of one approach over the other.

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“…which holds due to Bellman's principle of optimality (see [29], Chapter 6). As the minimization is performed, the optimal control policy is also formed as µk pζq " arg min…”

Section: Control Objective and Dynamic Programming Solutionmentioning

confidence: 99%

Section: Wind Considerationsmentioning

confidence: 99%

Vision-based target tracking with a small UAV: Optimization-based control strategies

Quintero

Hespanha

2014

Control Engineering Practice

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“…It is known that solving Problem 3 directly is numerically unstable [24]. However, Theorem 1 suggests an algorithmic approach to solving Problem 3, by making a discrete analog to a bang-bang control with a switching function.…”

Section: Construct the Lqt Problemmentioning

confidence: 99%

“…Let e * , λ * and u * be the optimal solution, by the necessary conditions for the optimality [24], we have:…”

Section: Construct the Lqt Problemmentioning

confidence: 99%

A Discrete Meta-Control Procedure for Approximating Solutions to Binary Programs

Kohn

Zabinsky

2013

Entropy

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Large-scale binary integer programs occur frequently in many real-world applications. For some binary integer problems, finding an optimal solution or even a feasible solution is computationally expensive. In this paper, we develop a discrete meta-control procedure to approximately solve large-scale binary integer programs efficiently. The key idea is to map the vector of n binary decision variables into a scalar function defined over a time interval [0, n] and construct a linear quadratic tracking (LQT) problem that can be solved efficiently. We prove that an LQT formulation has an optimal binary solution, analogous to a classical bang-bang control in continuous time. Our LQT approach can provide advantages in reducing computation while generating a good approximate solution. Numerical examples are presented to demonstrate the usefulness of the proposed method.

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“…Optimal control problems for nonlinear systems have been developed widely in aerospace control, process control, vehicles, and numerous other applications [1,2]. A core challenge of deriving the optimal controller for nonlinear systems is that it often fails to solve the underlying Hamilton-Jacobi-Bellman (HJB) equation.…”

Section: Introductionmentioning

confidence: 99%

Data‐Driven Adaptive Critic Approach for Nonlinear Optimal Control via Least Squares Support Vector Machine

Sun

Liu

2017

Asian Journal of Control

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This paper develops an online adaptive critic algorithm based on policy iteration for partially unknown nonlinear optimal control with infinite horizon cost function. In the proposed method, only a critic network is established, which eliminates the action network, to simplify its architecture. The online least squares support vector machine (LS-SVM) is utilized to approximate the gradient of the associated cost function in the critic network by updating the input-output data. Additionally, a data buffer memory is added to alleviate computational load. Finally, the feasibility of the online learning algorithm is demonstrated in simulation on two example systems.

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Optimal Control

Cited by 1,818 publications

References 0 publications

Vision-based target tracking with a small UAV: Optimization-based control strategies

Vision-based target tracking with a small UAV: Optimization-based control strategies

A Discrete Meta-Control Procedure for Approximating Solutions to Binary Programs

Data‐Driven Adaptive Critic Approach for Nonlinear Optimal Control via Least Squares Support Vector Machine

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