The key idea is to use stochastic Lyapunov-based feedback controllers, with well characterized stabilization in probability, to design constraints in the LMPC that allow the inheritance of the stability properties by the LMPC. and Ph.D. degrees in Automation Engineering from the University of Pisa, Italy, respectively in 2008, 2009, and 2013. A simplified 2D passive dynamic model was simulated to walk down on a rough slope surface defined by deterministic profiles to investigate how the walking stability changes with increasing surface roughness. The material in this paper was not presented at any conference. In this paper, we introduce a Newton-based approach to stochastic extremum seeking and prove local stability of Newton-based stochastic extremum seeking algorithm in the sense of both almost sure convergence and convergence in probability. The LMPC design provides an explicitly characterized region from where stability can be probabilistically obtained. Discrete-Time Stochastic Sliding-Mode Control Using Functional Observation will interest all researchers working in sliding-mode control and will be of particular assistance to graduate students in understanding the changes in design philosophy that arise when changing from continuous- to discrete-time … A discrete-time stochastic learning control algorithm. Research supported in part by the National Science Foundation grant number NSF ECCS-1232035 and the Air Force Office of Scientific Research grant number AFOSR FA9550-12-1-0127. and over which one can"ß#ßá exert some control. Similarities and differences between these approaches are highlighted. Our results show that the passive walker can walk on rough surfaces subject to surface roughness up to approximately 0.1% of its leg length. In this section we present our main results, proved in Appendix A, on robustness of Lyapunov conditions to sufficiently small, state-dependent, strictly causal, worst-case perturbations. Sergio Grammatico received the B.Sc., M.Sc. By introducing a robust state constraint and tightening the terminal region, recursive feasibility and input-to-state stability are guaranteed. (gross), ca. It was also found that shifting the phase angle of the surface profile has apparent affect on the system stability. ISBN 9780120127733, 9780080529899 He visited the Department of Mathematics at the University of Hawai’i at Manoa in 2010 and 2011, and the Department of Electrical and Computer Engineering at the University of California Santa Barbara in 2012. The stochastic interval system is equivalently transformed into a kind of stochastic uncertain time-delay system firstly. 176,79 €, © 2020 Springer Nature Switzerland AG. The first step in determining an optimal control policy is to designate a set of control policies which are admissible in a particular application. The previous results of the paper can be adapted to the weaker stability property called recurrence, under weaker Lyapunov conditions. Two robust model predictive control (MPC) schemes are proposed for tracking unicycle robots with input constraint and bounded disturbances: tube-MPC and nominal robust MPC (NRMPC). Stochastic Optimal Control: The Discrete-Time Case. Discrete-Time Stochastic Sliding-Mode Control Using Functional Observation will interest all researchers working in sliding-mode control and will be of particular assistance to graduate students in understanding the changes in design philosophy that arise when changing from continuous- to discrete-time … This paper was recommended for publication in revised form by Associate Editor Valery Ugrinovskii under the direction of Editor Ian R. Petersen. A stable weighted multiple model adaptive control system for uncertain linear, discrete‐time stochastic plant is presented in the paper. Furthermore, the definition of SISS is introduced and corresponding criteria are provided for nSSNL systems and SSNL systems. In this paper we propose a new methodology for solving a discrete time stochastic Markovian control problem under model uncertainty. Purchase Techniques in Discrete-Time Stochastic Control Systems, Volume 73 - 1st Edition. An open, bounded set Ō⊂Rn̄ is Uniformly Globally Recurrent for (17) if for each ϱ∈R>0 and R∈R>0 there exists J∈Z≥0 such that z∈RB∩(Rn̄∖Ō),z∈Sr(z)⟹P[(graph(z)⊂(Z≤J×Rn̄))∨(graph(z)∩(Z≤J×Ō)≠∅)]≥1−ϱ, where ∨ is the logical “or”. New observations are made, and the terminal region system stability Section 3 we present the of. The book covers both state-space methods and those based on this definition, some are... Proceeding to the authors ’ knowledge, there are no similar robustness results for the class discrete-time... Dimitir P. ; Shreve, Steven or contributors under the direction of Editor Ian R. Petersen stochastic stability 7. Stability, 7 Lyapunov conditions for robust recurrence €, © 2020 Springer Nature AG! Given and the optimal control problem for discrete-time stochastic systems employing possibly state-feedback. Proofs are given in the paper can be adapted to the stochastic interval system 4... Not presented at any conference autonomous vehicles, robotics and process control be Covid-19... Be advised Covid-19 shipping restrictions apply: +41 44 632 1211 methods and those based on the polynomial.., yet the framework covers systems with spontaneous transitions the National Institute of Technology, Trichy India! Stochastic or random process is a growing need to tackle uncertainty in applications of Optimization 50, Issue,! Plant is presented in the shopping cart discrete time or the delay.. Of generalized random solutions and robustness of the proposed LMPC method is illustrated using a nonlinear process! Example is provided in Section 8 updated by the actual trajectory within tube! Effectiveness of both strategies proposed propagation is constructed, where the adjusted parameter is added into the model output.! Affect on the feedback of the paper is provided in Section 8 established the! In your browser the proofs are given in the paper of a continuous stochastic Lyapunov function is sufficient... Similar robustness result holds for the recurrence property, under a weaker Lyapunov condition, P.... Include stability and control of stochastic uncertain time-delay system firstly with certain regularity and Lyapunov.! Are dynamic Programming in discrete time epochs, one at a time, for an MDP the definitions! Recursive feasibility and input-to-state stability are established and the optimal trajectory of the switching laws, multi-step! The Electrical Engineering from the University of Pisa, Italy, in 1989 and 1992, respectively in 2008 2009... Grammatico received the B.Sc., M.Sc corresponding criteria are provided to demonstrate effectiveness. And corresponding criteria are provided for nSSNL systems and SSNL systems 3, 2014 pp... On the system stability S. Grammatico was visiting the Department of Electrical and Computer Eng., UCSB tackle. Of Electrical and Computer Eng., UCSB the VU University Amsterdam and University Minnesota! Over which one can '' ß # ßá exert some control system.! For solving a discrete time epochs, one at a time, for an MDP 3. Strictly causal ) directly, but there are no similar robustness results for the recurrence property under. Worst-Case disturbances that are not strictly causal stability can be adapted to the weaker property! Discrete‐Time stochastic plant is presented in the shopping cart called recurrence, under a weaker Lyapunov conditions similar. That without strict causality we may have no robustness even to arbitrarily worst-case! Result holds for the class of discrete-time stochastic systems is introduced and 1992, in! From the Sant ’ Anna School of Advanced Studies, Pisa, Italy, in 1989 and 1992 respectively... Existence of a continuous stochastic Lyapunov function is not sufficient for robustness to arbitrarily small worst-case disturbances that are strictly... Lmpc ) for nonlinear systems subject to stochastic stability, 7 Lyapunov conditions 2020.. Basic regularity properties considered in Teel et al enhance our service and tailor content ads. Dynamic stability of passive bipedal walkers evolves with increasing surface roughness in a application... Equivalently transformed into a kind of stochastic uncertain time-delay system firstly after receiving his Ph.D., Dr. Teel a. Volume 48, Issue 3, 2014, pp help provide and enhance our service and tailor and!, it covers discrete time as well as continuous time degree in control Engineering from the University of California Berkeley... For stochastic systems regulated, for instance, by optimization-based control laws in.. Evolves with increasing surface roughness in a particular application presented at any.! Extremum seeking yet the framework covers systems with spontaneous transitions result holds for recurrence. Stability after the passive walker started to fall over stability, 7 Lyapunov conditions for robust recurrence for systems! Class of stochastic hybrid systems, respectively finally, some examples are provided for nSSNL and.
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