ABSTRACT
We consider an anytime control algorithm for the situation when the processor resource availability is time-varying. The basic idea is to calculate the components of the control input vector sequentially to maximally utilize the processing resources available at every time step. Thus, the system evolves as a discrete time hybrid system with the particular mode active at any time step being dictated by the processor availability. We extend our earlier work to consider the sequence in which the control inputs are calculated as a variable. In particular, we propose stochastic decision rules in which the inputs are chosen according to a Markov chain. For the LQG case, we present a Markovian jump linear system based formulation that provides analytical performance and stability expressions. For more general cases, we present a receding horizon control based implementation and illustrate the increase in performance through simulations.
- P. Antsaklis and J. Baillieul. Special issue on networked control systems. IEEE Transactions on Automatic Control, 49(9):1421--1423, 2004.Google ScholarCross Ref
- P. Antsaklis and J. Baillieul. Special issue on networked control systems. Proceedings of the IEEE, 95(1):9--28, 2007.Google ScholarCross Ref
- R. Bhattacharya and G. J. Balas. Anytime control algorithms: Model reduction approach. AIAA Journalof Guidance, Control and Dynamics, 27(5):767--776, 2004.Google ScholarCross Ref
- M. Caccamo, G. Buttazzo, and L. Sha. Handling execution overruns in hard real-time control systems. IEEE Transactions on Computers, 51(7):835--849, July 2002. Google ScholarDigital Library
- M. Cannon, V. Deshmukh, and B. Kouvaritakis. Nonlinear model predictive control with polytopic invariant sets. Automatica, 39:1487--1494, 2003. Google ScholarDigital Library
- A. Cervin, J. Eker, B. Bernhardsson, and K.-E. Arzen. Feedback-feedforward scheduling of control tasks. Real-Time Systems, 23(1--2):25--53, 2002. Google ScholarDigital Library
- O. L. V. Costa, M. D. Fragoso, and R. P. Marques. Discrete-Time Markov Jump Linear Systems. Springer, Series: Probability and its Applications, 2005.Google Scholar
- D. Goldfarb and S. Liu. An o(n3l) primal interior point algorithm for convex quadratic programming. Mathematical Programming, 49:325--340, 1991. Google ScholarDigital Library
- L. Greco, D. Fontanelli, and A. Bicchi. Almost sure stability of anytime controllers via stochastic scheduling. In Proceedings of the IEEE Int. Conf. on Decision and Control, pages 5640--5645, December 2007.Google ScholarCross Ref
- G. Grimm, M. J. Messina, S. E. Tuna, and A. R. Teel. Examples when nonlinear model predictive control is nonrobust. Automatica, 40:1729--1738, 2004. Google ScholarDigital Library
- V. Gupta. On an anytime algorithm for control. In Proceedings of the IEEE Int. Conf. on Decision and Control, December 2009.Google ScholarCross Ref
- D. Henriksson and J. Akesson. Flexible implementation of model predictive control using sub-optimal solutions. Technical Report TFRT-7610-SE, Department of Automatic Control, Lund University, April 2004.Google Scholar
- D. Henriksson, A. Cervin, J. Akesson, and K. E. Arzen. On dynamic real-time scheduling of model predictive controllers. In Proceedings of the 41st IEEE Conference on Decision and Control, December 2002.Google ScholarCross Ref
- E. J. Horvitz. Computation and Action under Bounded Resources. PhD thesis, Department of Computer Science and Medicine, Stanford University, 1990. Google ScholarDigital Library
- X. Huang and A. M. K. Cheng. Applying imprecise algorithms to real-time image and video transmission. In Proceedings of the International Conference on Parallel and Distributed Systems, pages 96--101, 1995. Google ScholarDigital Library
- E. C. Kerrigan and J. M. Maciejowski. Robust feasibility in model predictive control: Necessary and sufficient conditions. In Proc. IEEE Conference on Decision and Control, pages 728--733, December 2001.Google ScholarCross Ref
- D. Liu, X. Hu, M. Lemmon, and Q. Ling. Scheduling tasks with markov-chain constraints. In Proceedings of the 17th Euromicro Conference on Real-time Systems, July 2005. Google ScholarDigital Library
- L. K. McGovern and E. Feron. Requirements and hard computational bounds for real-time optimization in safety critical control systems. In Proceedings of the IEEE Conference on Decision and Control, 1998.Google ScholarCross Ref
- L. K. McGovern and E. Feron. Closed-loop stability of systems driven by real-time dynamic optimization algorithms. In Proceedings of the IEEE Conference on Decision and Control, 1999.Google ScholarCross Ref
- V. Millan--Lopez, W. Feng, and J. W. S. Liu. Using the imprecise computation technique for congestion control on a real-time traffic switching element. In Proc. of the International Conference on Parallel and Distributed Systems, pages 202--208, 1994. Google ScholarDigital Library
- D. E. Quevedo, E. I. Silva, and G. Goodwin. Packetized predictive control over erasure channels. In Proc. of the American Control Conference, 2007.Google ScholarCross Ref
- D. M. Raimondo, D. Limon, M. Lazar, L. Magni, and E. F. Camacho. Min-max model predictive control of nonlinear systems: A unifying overview on stability. European Journal of Control, 15(1), 2009.Google ScholarCross Ref
- D. Seto, J. Lehoczky, L. Sha, and K. Shin. On task schedulability in real-time control system. In Proc. IEEE Real-Time Systems Symp., December 1996. Google ScholarDigital Library
- P. Tabuada. Event-triggered real-time scheduling of stabilizing control tasks. IEEE Transactions on Automatic Control, 52(9):1680--1685, September 2007.Google ScholarCross Ref
- X. Wang and M. D. Lemmon. Self-triggered feedback control systems with finite-gain l2 stability. IEEE Transactions on Automatic Control, 45(3), March 2009.Google Scholar
- H. Yoshomito, D. Arita, and R. Taniguchi. Real-time communication for distributed vision processing based on imprecise computation model. In Proceedings of International Parallel and Distributed Processing Symposium, pages 128--133, 1992.Google Scholar
- T. Zhou, X. Hu, and E.-M. Sha. A probabilistic performance metric for real-time system design. In Proc. of the 7th International Workshop on Hardware-Software Codesign (CODES) (ACM/IEEE), pages 90--94, May 1999. Google ScholarDigital Library
- S. Zilberstein. Using anytime algorithms in intelligent systems. Artificial Intelligence Magazine, 17(3):73--83, 1996.Google Scholar
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- On a control algorithm for time-varying processor availability
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