On Converting Optimal Control Problems into Nonlinear Programming Problems

Kraft, Dieter

doi:10.1007/978-3-642-82450-0_9

Cited by 149 publications

(76 citation statements)

References 26 publications

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“…Some of the basic ideas of this discretization scheme have been formerly outlined by Kraft [14] and Hargraves and Paris [11]. A discretization of the time interval 0 = t 1 < t 2 < .…”

mentioning

confidence: 99%

Numerical Solution of Optimal Control Problems by Direct Collocation

1993

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Abstract. By an appropriate discretization of control and state variables, a constrained optimal control problem is transformed into a finite dimensional nonlinear program which can be solved by standard SQP-methods [10]. Convergence properties of the discretization are derived. From a solution of this method known as direct collocation, these properties are used to obtain reliable estimates of adjoint variables. In the presence of active state constraints, these estimates can be significantly improved by including the switching structure of the state constraint into the optimization procedure. Two numerical examples are presented.

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“…Some of the basic ideas of this discretization scheme have been formerly outlined by Kraft [14] and Hargraves and Paris [11]. A discretization of the time interval 0 = t 1 < t 2 < .…”

mentioning

confidence: 99%

Numerical Solution of Optimal Control Problems by Direct Collocation

1993

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“…There are three basic approaches for addressing optimal control problems, that is, DP, direct methods [24,25] and indirect methods [26,27]. DP adopts the principle of optimality of subarcs to recursively compute feedback control.…”

Section: Dynamic Programming (Dp) Implementationmentioning

confidence: 99%

Dynamic Eco-Driving Speed Guidance at Signalized Intersections: Multivehicle Driving Simulator Based Experimental Study

Chen

Yan

Sun

et al. 2018

Journal of Advanced Transportation

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Variations in vehicle fuel consumption and gas emissions are usually associated with changes in cruise speed and the aggressiveness of drivers' acceleration/deceleration, especially at traffic signals. In an attempt to enhance vehicle fuel efficiency on arterials, this study developed a dynamic eco-driving speed guidance strategy (DESGS) using real-time signal timing and vehicle positioning information in a connected vehicle (CV) environment. DESGS mainly aims to optimize the fuel/emission speed profiles for vehicles approaching signalized intersections. An optimization-based rolling horizon and a dynamic programming approach were proposed to track the optimal guided velocity for individual vehicles along the travel segment. In addition, a vehicle specific power (VSP) based approach was integrated into DESGS to estimate the fuel consumption and CO 2 emissions. To evaluate the effectiveness of the overall strategy, 15 experienced drivers were recruited to participate in interactive speed guidance experiments using multivehicle driving simulators. It was found that compared to vehicles without speed guidance, those with DESGS had a significantly reduced number of stops and approximately 25% less fuel consumption and CO 2 emissions.

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“…Direct methods, on the other hand, rely on a priori discretization of the control trajectories. Two main classes of direct methods are (i) the simultaneous method, where the dynamic model is also discretized, using e.g., collocation techniques and extra optimization variables [4], to arrive at a fully algebraic model and (ii) the sequential method, where the dynamic model is retained, and instead is resolved using numerical integration [5]. The focus in this work is on the sequential method that has shown capabilities for handling large-scale, stiff problems with high accuracy [6], arguably due to keeping the problem dimension relatively small [7] and the use of adaptive numerical integrators furnished with error control mechanisms.…”

Section: Introductionmentioning

confidence: 99%

Efficient Control Discretization Based on Turnpike Theory for Dynamic Optimization

Sahlodin

Barton

2017

Processes

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Dynamic optimization offers a great potential for maximizing performance of continuous processes from startup to shutdown by obtaining optimal trajectories for the control variables. However, numerical procedures for dynamic optimization can become prohibitively costly upon a sufficiently fine discretization of control trajectories, especially for large-scale dynamic process models. On the other hand, a coarse discretization of control trajectories is often incapable of representing the optimal solution, thereby leading to reduced performance. In this paper, a new control discretization approach for dynamic optimization of continuous processes is proposed. It builds upon turnpike theory in optimal control and exploits the solution structure for constructing the optimal trajectories and adaptively deciding the locations of the control discretization points. As a result, the proposed approach can potentially yield the same, or even improved, optimal solution with a coarser discretization than a conventional uniform discretization approach. It is shown via case studies that using the proposed approach can reduce the cost of dynamic optimization significantly, mainly due to introducing fewer optimization variables and cheaper sensitivity calculations during integration.

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On Converting Optimal Control Problems into Nonlinear Programming Problems

Cited by 149 publications

References 26 publications

Numerical Solution of Optimal Control Problems by Direct Collocation

Numerical Solution of Optimal Control Problems by Direct Collocation

Dynamic Eco-Driving Speed Guidance at Signalized Intersections: Multivehicle Driving Simulator Based Experimental Study

Efficient Control Discretization Based on Turnpike Theory for Dynamic Optimization

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