Robust Trajectory Planning for Robotic Communications under Fading Channels

We consider a new problem of robust trajectory planning for robots that have a physical destination and a communication constraint. Specifically, the robot or automatic vehicle must move from a given starting point to a target point while uploading/downloading a given amount of data within a given time, while accounting for the energy cost and the time taken to download. However, this trajectory is assumed to be planned in advance (e.g., because online computation cannot be performed). Due to wireless channel fluctuations, it is essential for the planned trajectory to be robust to packet losses and meet the communication target with a sufficiently high probability. This optimization problem contrasts with the classical mobile communications paradigm in which communication aspects are assumed to be independent from the motion aspects. This setup is formalized here and leads us to determining non-trivial trajectories for the mobile, which are highlighted in the numerical result

Robust Trajectory Planning for Robotic Communications under Fading Channels

We consider a new problem of robust trajectory planning for robots that have a physical destination and a communication constraint. Specifically, the robot or automatic vehicle must move from a given starting point to a target point while uploading/downloading a given amount of data within a given time, while accounting for the energy cost and the time taken to download. However, this trajectory is assumed to be planned in advance (e.g., because online computation cannot be performed). Due to wireless channel fluctuations, it is essential for the planned trajectory to be robust to packet losses and meet the communication target with a sufficiently high probability. This optimization problem contrasts with the classical mobile communications paradigm in which communication aspects are assumed to be independent from the motion aspects. This setup is formalized here and leads us to determining non-trivial trajectories for the mobile, which are highlighted in the numerical result

Robust H2 Switched Filter Design For Discrete-time Polytopic Linear Parameter-varying Systems

This paper deals with a robust H2 filter design problem for discrete-time polytopic linear parameter-varying systems. The novelty is to design a set of full order filters and a switching rule to orchestrate them in order to assure an H2 performance index of the estimation error. The switched linear filter does not require the online measurement of the uncertain time-varying parameter which, in a great part of practical applications, is not available. The conditions are based on Lyapunov-Metzler inequalities with a special subclass of Metzler matrices. The proposed switched filter outperforms the ones available in the literature to date as far as the H2 norm of the estimation error is taken into account. The main theoretical implications of the switched filtering methodology in the framework of linear time-invariant uncertain systems and linear parameter-varying systems are discussed and illustrated by academical examples. © 2013 Elsevier B.V.979199Apkarian, P., Gahinet, P., A convex characterization of gain-scheduled H ∞ controllers (1995) IEEE Trans. Autom. Control, 40, pp. 853-864Daafouz, J., Bernussou, J., Geromel, J.C., On inexact LPV control design of continuous-time polytopic systems (2008) IEEE Trans. Autom. Control, 53, pp. 1674-1678Duan, Z., Zhang, J., Zhang, C., Mosca, E., Robust H2 and H ∞ filtering for uncertain linear systems (2006) Automatica, 42, pp. 1919-1926Deaecto, G.S., Geromel, J.C., Daafouz, J., Trajectory-dependent filter design for discrete-time switched linear systems (2010) Nonlinear Anal. Hybrid Syst., 4, pp. 1-8Deaecto, G.S., Geromel, J.C., H ∞ control for continuous-time switched linear systems (2010) ASME J. Dyn. Syst. Meas. Control, 132, pp. 1-7. , 041013Deaecto, G.S., Geromel, J.C., Daafouz, J., Dynamic output feedback H ∞ control of switched linear systems (2011) Automatica, 47, pp. 1713-1720Deaecto, G.S., Geromel, J.C., Daafouz, J., Switched state feedback control for continuous time-varying polytopic systems (2011) Int. J. Control, 84, pp. 1500-1508Deaecto, G.S., Fioravanti, A.R., Geromel, J.C., Suboptimal switching control consistency analysis for discrete-time switched linear systems (2013) Eur. J. Control, 19, pp. 214-219Deaecto, G.S., Geromel, J.C., H ∞ state feedback switched control for discrete time-varying polytopic systems (2013) Int. J. Control, 86, pp. 591-598Decarlo, R.A., Branicky, M.S., Pettersson, S., Lennartson, B., Perspectives and results on the stability and stabilizability of hybrid systems (2000) Proc. IEEE, 88, pp. 1069-1082Ding, D., Yang, G., Li, X., H-infinity filtering for discrete-time switched linear systems under arbitrary switching (2011) J. Control Theory Appl., 9, pp. 261-266Gao, H., Zhang, L., Shi, P., Mou, S., Wang, C., Stability and stabilization of switched linear discrete-time systems with polytopic uncertainties (2006) Proceedings of the 2006 American Control Conference, pp. 5953-5958. , MinnesotaGao, H., Meng, X., Chen, T., A new design of robust H2 filters for uncertain systems (2008) Syst. Control Lett., 57, pp. 585-593Geromel, J.C., De Oliveira, M.C., Bernussou, J., Robust filtering of discrete-time linear systems with parameter dependent Lyapunov functions (2002) SIAM J. Control Optim., 41, pp. 700-711Geromel, J.C., Colaneri, P., Stability and stabilization of discrete-time switched systems (2006) Int. J. Control, 79, pp. 719-728Geromel, J.C., Colaneri, P., Bolzern, P., Dynamic output feedback control of switched linear systems (2008) IEEE Trans. Autom. Control, 53, pp. 720-733Geromel, J.C., Deaecto, G.S., Daafouz, J., Suboptimal switching control consistency analysis for switched linear systems (2013) IEEE Trans. Autom. Control, 58, pp. 1857-1861Hu, K., Yuan, J., Improved robust H ∞ filtering for uncertain discrete-time switched systems (2009) IET Control Theory Appl., 3, pp. 315-324Hui, L., Tianshu, W., Tao, Z., Jingyan, S., H2 gain scheduled filtering for polytopic discrete-time linear parameter-varying systems (2009) International Conference on Computer and Automation Engineering, pp. 31-35Ji, Z., Wang, L., Xie, G., Quadratic stabilization of uncertain discrete-time switched systems via output feedback (2005) Circuits Syst. Signal Process., 24, pp. 733-751Leith, D.J., Leithead, W.E., Survey of gain-scheduling analysis and design (2000) Int. J. Control, 73, pp. 1001-1025Liberzon, D., Morse, A.S., Basic problems in stability and design of switched systems (1999) IEEE Control Syst. Mag., 19, pp. 59-70Liberzon, D., (2003) Switching in Systems and Control, , Birkhäuser Boston, USAMahmoud, M.S., Boujarwah, A.S., Robust H ∞ filtering for a class of linear parameter-varying systems (2001) IEEE Trans. Circuits Syst., 48, pp. 1131-1138Rugh, W.J., Shamma, J.S., Research on gain scheduling (2000) Automatica, 36, pp. 1401-1425Sato, M., Filter design for LPV systems using quadratically parameter-dependent Lyapunov functions (2006) Automatica, 42, pp. 2017-2023Shamma, J.S., Athans, M., Guaranteed properties of gain scheduled control for linear parameter-varying plants (1991) Automatica, 27, pp. 559-564De Souza, C.E., Barbosa, K.A., Trofino, A., Robust H ∞ filtering for discrete-time linear systems with uncertain time-varying parameters (2006) IEEE Trans. Signal Process., 54, pp. 2110-2118Sun, Z., Ge, S.S., (2005) Switched Linear Systems Control and Design, , Springer LondonTuan, H.D., Apkarian, P., Nguyen, T.Q., Robust and reduced-order filtering new LMI-based characterizations and methods (2001) IEEE Trans. Signal Process., 49, pp. 2975-2984Xie, L., Lu, L., Zhang, D., Zhang, H., Improved robust H2 and H ∞ filtering for uncertain discrete-time systems (2004) Automatica, 40, pp. 873-880Zhai, G., Lin, H., Antsaklis, P.J., Quadratic stabilizability of linear switched systems with polytopic uncertainties (2003) Int. J. Control, 76, pp. 747-753Zhang, J., Xia, Y., Shi, P., Parameter-dependent robust H ∞ filtering for uncertain discrete-time systems (2009) Automatica, 45, pp. 560-565Zhang, L., Shi, P., H ∞ filtering for a class of switched linear parameter varying systems (2011) Int. J. Syst. Sci., 42, pp. 781-788Wicks, M.A., Peleties, P., Decarlo, R.A., Construction of piecewise Lyapunov functions for stabilizing switched systems (1994) Proceedings of the 33rd IEEE Conference on Decision and Control, pp. 3492-3497. , Orlando, US

Dynamic Output Feedback H∞ Control Of Switched Linear Systems

This paper is devoted to dynamic output feedback H∞ control design of switched linear systems in both continuous and discrete-time domains. More specifically, the main purpose is to jointly design a switching rule and a full order dynamic output feedback switched controller that render the associated closed-loop switched linear system globally asymptotically stable and impose a pre-specified upper bound to the L2 gain. An example of practical importance is presented to illustrate the validity and efficiency of the theory. © 2011 Elsevier Ltd. All rights reserved.47817131720Blanchini, F., Savorgnan, C., Stabilizability of switched linear systems does not imply the existence of convex Lyapunov functions (2008) Automatica, 44, pp. 1166-1170Deaecto, G.S., Geromel, J.C., H∞ control for continuous-time switched linear systems (2010) Transactions of the ASME. Journal of Dynamic Systems, Measurement and Control, 132, p. 041013. , numberDecarlo, R.A., Branicky, M.S., Pettersson, S., Lennartson, B., Perspectives and results on the stability and stabilizability of hybrid systems (2000) Proceedings of the IEEE, 88, pp. 1069-1082Geromel, J.C., Colaneri, P., Stability and stabilization of continuous-time switched linear systems (2006) SIAM Journal on Control and Optimization, 45 (5), pp. 1915-1930. , DOI 10.1137/050646366Geromel, J.C., Colaneri, P., Stability and stabilization of discrete time switched systems (2006) International Journal of Control, 79, pp. 719-728Geromel, J.C., Colaneri, P., Bolzern, P., Dynamic output feedback control of switched linear systems (2008) IEEE Transactions on Automatic Control, 53 (3), pp. 720-733. , DOI 10.1109/TAC.2008.919860Geromel, J.C., Deaecto, G.S., Switched state feedback control for continuous-time uncertain systems (2009) Automatica, 45, pp. 593-597Geromel, J.C., Korogui, R.H., Bernussou, J., H2 and H∞ robust output feedback control for continuous time polytopic systems (2007) IET Control Theory and Applications, 1 (5), pp. 1541-1549. , DOI 10.1049/iet-cta:20060460Hespanha, J.P., Morse, A.S., Switching between stabilizing controllers (2002) Automatica, 38, pp. 1905-1917Ji, Z., Guo, X., Wang, L., Xie, G., Robust H∞ control and stabilization of uncertain switched linear systems: A multiple lyapunov functions approach (2006) Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME, 128 (3), pp. 696-700. , DOI 10.1115/1.2238874Ji, Z., Wang, L., Xie, G., Quadratic stabilization of uncertain discrete-time switched systems via output feedback (2005) Circuits, Systems, and Signal Processing, 24 (6), pp. 733-751. , DOI 10.1007/s00034-005-0920-2Liberzon, D., (2003) Switching in Systems and Control, , BirkhuserLiberzon Daniel, Morse A.Stephen, Basic problems in stability and design of switched systems (1999) IEEE Control Systems Magazine, 19 (5), pp. 59-70. , DOI 10.1109/37.793443Lin, H., Antsaklis, P.J., Hybrid state feedback stabilization with l2 performance for discrete-time switched linear systems (2008) International Journal of Control, 81, pp. 1114-1124Lin, H., Antsaklis, P.J., Stability and stabilizability of switched linear systems: A survey of recent results (2009) IEEE Transactions on Automatic Control, 54, pp. 308-322Scherer, C., Gahinet, P., Chilali, M., Multiobjective output-feedback control via LMI optimization (1997) IEEE Transactions on Automatic Control, 42 (7), pp. 896-911. , PII S0018928697050691Shorten, R., Wirth, F., Mason, O., Wulff, K., King, C., Stability criteria for switched and hybrid systems (2007) SIAM Review, 49 (4), pp. 545-592. , DOI 10.1137/05063516XSun, Z., Ge, S.S., (2005) Switched Linear Systems: Control and Design, , Springer LondonVan Der Schaft, A.J., Schumacher, J.M., (2000) An Introduction to Hybrid Dynamical Systems, , SpringerZhai, G., Hu, B., Yasuda, K., Michel, A.N., Disturbance attenuation properties of time-controlled switched systems (2001) Journal of the Franklin Institute, 338 (7), pp. 765-779. , DOI 10.1016/S0016-0032(01)00030-8, PII S0016003201000308Zhai, G., Lin, H., Kim, Y., Imae, J., Kobayashi, T., L2 gain analysis for switched systems with continuous-time and discrete-time subsystems (2005) International Journal of Control, 78 (15), pp. 1198-1205. , DOI 10.1080/00207170500274966Zhao, J., Hill, D.J., On stability L2 gain and H∞ control for switched systems (2008) Automatica, 44, pp. 1220-123

A simple approach for switched control design with control bumps limitation

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)By its own nature, control of switched systems in general leads to expressive discontinuities at switching times. Hence, this class of dynamic systems needs additional care as far as implementation constraints such as for instance control amplitude limitation is concerned. This paper aims at providing numerically tractable conditions to be incorporated in the control design procedure in order to reduce control bumps. The switching strategy and continuous control laws are jointly determined as well as an Jew guaranteed cost is minimized. Due to its theoretical and practical importance, special attention is given to the dynamic output feedback control design problem. The results are illustrated by means of examples borrowed from the literature which are also used for comparisons that put in evidence the efficiency of the proposed strategy. (C) 2012 Elsevier B.V. All rights reserved.611212151220ANR [ANR-2008 SEGI 004]European project HYCON2Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)ANR [ANR-2008 SEGI 004

Switched state-feedback control for continuous time-varying polytopic systems

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)This article deals with switched state-feedback H(2) control design of continuous time-varying polytopic systems. More specifically, the main goal is to determine, simultaneously, a set of state-feedback gains and a switching rule to orchestrate them, rendering the closed-loop system globally asymptotically stable for all time-varying uncertain parameter under consideration and assuring a guaranteed H(2) cost. A contribution of the present switched control technique compared to the gain scheduling, widely used in the literature, is that the online measurement of the uncertain parameter is not required and no assumption on its time derivative is imposed. The conditions are based on modified Lyapunov-Metzler inequalities and can be solved by line search coupled with LMIs. An academic example illustrates the theoretical results and compares the present technique with other techniques from literature.84915001508Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)ANR [ANR-2008 SEGI 004 01-30011459]Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)ANR [ANR-2008 SEGI 004 01-30011459