Optimal Control of State-Space Systems with Hard Bounds on Control Inputs and State Variables

Matthew Harker, Gerhard Rath, Johannes Handler

Research output: Chapter in Book/Report/Conference proceedingConference contribution


This paper presents a new numerical method for treating the problem of optimal control when there are hard bounds on the control variables (e.g., limit switches on a linear drive, current limits to motor input, etc.) and/or on the state/output variables (e.g., obstacle avoidance). This is accomplished by means of a new approach for discretizing the optimal control problem, while introducing regularization terms to reduce the solution space to smooth functions. Further, by introducing a consistent discretization of the state-space equations with arbitrary boundary conditions, the problem is cast as a problem of quadratic programming, whereby (hard) bounds can be put on any of the state-space variables (i.e., input or output). The method is demonstrated on the example of a pendulum on a cart. Bounded optimal control solutions are computed for two examples: Velocity bounds are placed on the cart in the classic optimal control problem; a variation of trajectory tracking where instead of specifying a single valued path, the bounds of the trajectory of the pendulum bob are specified, and the required input to keep the bob within these bounds during its motion is computed.
Original languageEnglish
Title of host publication2023 12th Mediterranean Conference on Embedded Computing (MECO)
PublisherPubl by IEEE
Publication statusPublished - 6 Jun 2023
Event12th Mediterranean Conference on Embedded Computing (MECO) - Budva, Montenegro
Duration: 6 Jun 202310 Jun 2023
Conference number: 12


Conference12th Mediterranean Conference on Embedded Computing (MECO)
Abbreviated titleMECO

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