TY - GEN

T1 - Optimal Control of State-Space Systems with Hard Bounds on Control Inputs and State Variables

AU - Harker, Matthew

AU - Rath, Gerhard

AU - Handler, Johannes

N1 - Conference code: 12

PY - 2023/6/6

Y1 - 2023/6/6

N2 - 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.

AB - 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.

U2 - 10.1109/MECO58584.2023.10154995

DO - 10.1109/MECO58584.2023.10154995

M3 - Conference contribution

BT - 2023 12th Mediterranean Conference on Embedded Computing (MECO)

T2 - 12th Mediterranean Conference on Embedded Computing (MECO)

Y2 - 6 June 2023 through 10 June 2023

ER -