A method for constructing an optimal control strategy in a linear terminal problem

This paper deals with an optimal control problem for a linear discrete system subject to unknown bounded disturbances, where the control goal is to steer the system with guarantees into a given terminal set while minimising the terminal cost function. We define an optimal control strategy which takes into account the state of the system at one future time instant and propose an efficient numerical method for its construction. The results of numerical experiments show an improvement in performance under the optimal control strategy in comparison to the optimal open-loop worst-case control while maintaining comparable computation times.

Download Full-text

A closed-loop strategy in an optimal guaranteed control problem for a linear system

Doklady of the National Academy of Sciences of Belarus ◽

10.29235/1561-8323-2020-64-5-519-525 ◽

2020 ◽

Vol 64 (5) ◽

pp. 519-525

Author(s):

Dz. A. Kastsiukevich ◽

N. M. Dmitruk

Keyword(s):

Optimal Control ◽

Control Problem ◽

Time Instant ◽

Optimal Control Strategy ◽

Guaranteed Control ◽

Linear Discrete System ◽

Control Goal ◽

Bounded Disturbances ◽

Target Set ◽

Account Information

This paper deals with an optimal control problem for a linear discrete system subject to unknown bounded disturbances with the control goal being to steer the system with guarantees to a given target set while minimizing a given cost function. We define an optimal control strategy with one correction time instant, meaning taking into account information about one future state of the object, and propose an efficient numerical method for constructing it.

Download Full-text

A Comfort Oriented Control Strategy for Semi-Active Suspensions Based on Half Car Model

ASME 2010 Dynamic Systems and Control Conference, Volume 2 ◽

10.1115/dscc2010-4172 ◽

2010 ◽

Cited By ~ 12

Author(s):

Cristiano Spelta ◽

Diego Delvecchio ◽

Sergio M. Savaresi

Keyword(s):

Optimal Control ◽

Control Strategy ◽

Optimal Performance ◽

Optimal Control Strategy ◽

Active Suspensions ◽

Quarter Car Model ◽

Car Model ◽

Control Goal ◽

Quarter Car ◽

Effective Description

This paper is devoted to the design of a novel semi-active comfort-oriented control strategy based on the “half-car” modeling of the vehicle. The half car model is an effective description of the vertical behaviors in a vehicle like a motorcycle, since it is able to represent both the heave and pitch dynamics. A recent control strategy (the “Mix-1-Sensor”) have been proven to be the quasi-optimal control strategy when the system is described with a quarter car model and the comfort objective is the control goal. This paper presents an analysis of the performances of the Mix-1-Sensor implemented in a half car: this strategy is able to guarantee a quasi optimal performance in terms of heave dynamics but it is not able to manage the pitch dynamics efficiently. A pitch-oriented extension of this strategy is proposed in order to guarantee a better filtering of the pitch dynamics.

Download Full-text

Closed-Loop Optimal Control Strategy for Cancer Chemotherapy

Volume 9: Mechanical Systems and Control, Parts A, B, and C ◽

10.1115/imece2007-43527 ◽

2007 ◽

Author(s):

Barathram Ramkumar ◽

D. Subbaram Naidu

Keyword(s):

Optimal Control ◽

Cancer Cells ◽

Cancer Chemotherapy ◽

Nonlinear Model ◽

Control Strategy ◽

Closed Loop ◽

Drug Level ◽

Open Loop ◽

The Body ◽

Optimal Control Strategy

Cancer chemotherapy is the treatment of cancer using drugs that kill the cancer cells, when the drugs are administered either orally or through veins. The drugs are delivered according to a schedule so that a particular dosage of drug level is maintained in the body. The disadvantage of these drugs is that they not only kill the cancer cells but also kill the normal healthy cells. The role of optimal control in chemotherapy is to maintain an optimum amount of drug level in the body so that only cancer cells are killed and hence the effect of drug on the healthy cells is minimized. Three different mathematical models for cancer growth are considered: log-kill hypothesis, Norton-simon model, and Emax model. Two different cost functions are considered for constrained and unconstrained optimal control, respectively. An open loop optimal control strategy has been reported in the literature. In this paper, a closed-loop optimal control strategy is addressed using all the three models and for both the cases of constrained and unconstrained drug delivery. For the unconstrained case the original nonlinear model has been linearized and the closed loop design is obtained by using matrix Riccati solutions. On the other hand, for the constrained case the original nonlinear model has been used to obtain closed loop optimal control using bang-bang strategy. Final simulation results show the advantages of closed loop implementation in terms of simpler and elegant controller design and incorporating the effect of current state variations.

Download Full-text

Time-Optimal Control of Flexible Robots Made Robust Through Wave-Based Feedback

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.4002714 ◽

2010 ◽

Vol 133 (1) ◽

Cited By ~ 8

Author(s):

William J. O’Connor ◽

David J. McKeown

Keyword(s):

Optimal Control ◽

Control Strategy ◽

Robustness Analysis ◽

Optimal Solution ◽

Open Loop ◽

Time Optimal Control ◽

System Model ◽

Optimal Control Strategy ◽

Modeling Errors ◽

Time Optimal

This paper presents a new, robust, time-optimal control strategy for flexible manipulators controlled by acceleration-limited actuators. The strategy is designed by combining the well-known, open-loop, time-optimal solution with wave-based feedback control. The time-optimal solution is used to design a new launch wave input to the wave-based controller, allowing it to recreate the time-optimal solution when the system model is exactly known. If modeling errors are present or a real actuator is used, the residual vibrations, which would otherwise arise when using the time-optimal solution alone, are quickly suppressed due to the additional robustness provided by the wave-based controller. A proximal time-optimal response is still achieved. A robustness analysis shows that significant improvements can be achieved using wave-based control in conjunction with the time-optimal solution. The implications and limits are also discussed.

Download Full-text