Finite Set Control Transcription for Optimal Control Applications

Stanton, Stuart A.

doi:10.2514/1.44056

Cited by 10 publications

(5 citation statements)

References 47 publications

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“…Note that many real‐world applications from various engineering disciplines can be studied in the modeling framework that incorporates fixed‐level control inputs. The corresponding dynamic models represent an extremely wide range of systems of practical interest (see, e.g., ) and are accepted as realistic abstractions in industrial electronics, power systems engineering, aircrafts control engineering, and communication theory. Let us also emphasize the aerospace control applications of the mathematical models that include fixed‐level control inputs .…”

Section: Discussionmentioning

confidence: 99%

“…The corresponding dynamic models represent an extremely wide range of systems of practical interest (see, e.g., ) and are accepted as realistic abstractions in industrial electronics, power systems engineering, aircrafts control engineering, and communication theory. Let us also emphasize the aerospace control applications of the mathematical models that include fixed‐level control inputs . In fact, many modern application domains involve complex systems with switched‐type control design in which sub‐systems interconnections, mode‐transitions, and heterogeneous computational devices are presented.…”

Section: Discussionmentioning

confidence: 99%

“…We study a class of OCPs with quadratic costs functionals. The given structure of the admissible control function under consideration is mainly motivated by some important practical control applications (see ) as well as by the wide applicable modern quantization procedure associated with the original system dynamics (see, e.g., ). Note that some classes of optimal control with piecewise constraints was studied earlier.…”

Section: Introductionmentioning

confidence: 99%

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Optimal fixed-levels control for nonlinear systems with quadratic cost-functionals

Azhmyakov

Martínez

Poznyak

2015

Optim. Control Appl. Meth.

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SUMMARYThis paper is devoted to general optimal control problems (OCPs) associated with a family of nonlinear continuous-time switched systems in the presence of some specific control constraints. The stepwise (fixed-level type) control restrictions we consider constitute a common class of admissible controls in many real-world engineering systems. Moreover, these control restrictions can also be interpreted as a result of a quantization procedure appglied to the inputs of a conventional dynamic system. We study control systems with a priori given time-driven switching mechanism in the presence of a quadratic cost functional. Our aim is to develop a practically implementable control algorithm that makes it possible to calculate approximating solutions for the class of OCPs under consideration. The paper presents a newly elaborated linear quadratic-type optimal control scheme and also contains illustrative numerical examples.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimal fixed-levels control for nonlinear systems with quadratic cost-functionals

Azhmyakov

Martínez

Poznyak

2015

Optim. Control Appl. Meth.

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“…The aim of our contribution is to elaborate a consistent computational algorithm for an LQ-type OCP in the presence of piecewise constant control inputs. The given restrictive structure of the admissible control function under consideration is motivated by some important engineering applications (see [22,25,36]) as well as by the possible quantization procedure applied to the original dynamics (see e.g., [12,26]). Note that quadratic optimal control of piecewise linear systems was addressed earlier in [8,32].…”

Section: Introductionmentioning

confidence: 99%

Optimal LQ-Type Switched Control Design for a Class of Linear Systems with Piecewise Constant Inputs

Azhmyakov

Reincke-Collon

2014

IFAC Proceedings Volumes

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“…A similar approach is proposed in (9), where the time for each discrete control value on a given time horizon is optimized. At this, it resembles the VTT approach but does not incorporate a modification of the integration speed.…”

mentioning

confidence: 97%

Optimal Control Framework for Impulsive Missile Interception Guidance

Walter

Schlöffel

Holzapfel

2013

AIAA Guidance, Navigation, and Control (GNC) Conference

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An optimal control framework is presented that provides an endgame guidance scheme for the exo-atmospheric interception of hostile intercontinental missiles. Therein, a receding horizon optimization strategy is deployed, using a multiple shooting discretization of the dynamic system. The control parameterization is based on a specific endgame heuristic, so that acceleration commands can be approximated by a tangens hyperbolicus formulation to emulate the discrete structure of impulsive thruster acceleration commands. As a result, the number of optimization variables is significantly reduced, potentially enabling closed-loop control schemes. As a closed-loop algorithm, a modified nonlinear model predictive control approach is proposed. Numerical investigations are presented that address the endgame problem in the simplified environment of an interception plane. Nomenclature= acceleration vector of the kill vehicle = maximum acceleration of the kill vehicle = steepness of the tangens hyperbolicus approximation = correction angle, i.e. the angle between relative position and relative velocity = error compensation term = objective function of the nonlinear optimization problem = multi-dimensional ordinary differential equation for the system's state variables = equality constraint function of the nonlinear optimization problem = inequality constraint function of the nonlinear optimization problem = performance index of the optimal control problem = Lagrange term of the performance index = relative position vector of kill and reentry vehicle = position vector of the kill vehicle = position vector of the reentry vehicle (target) = position of the predicted intercept point (PIP) = control vector of the optimal control problem = relative velocity vector of kill and reentry vehicle = differential system state variables = maneuver angle, i.e. the angle between acceleration and relative position

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Finite Set Control Transcription for Optimal Control Applications

Cited by 10 publications

References 47 publications

Optimal fixed-levels control for nonlinear systems with quadratic cost-functionals

Optimal fixed-levels control for nonlinear systems with quadratic cost-functionals

Optimal LQ-Type Switched Control Design for a Class of Linear Systems with Piecewise Constant Inputs

Optimal Control Framework for Impulsive Missile Interception Guidance

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