Although control Lyapunov functions (CLFs) provide a mature framework for the synthesis of stabilizing controllers, their application in the field of hybrid systems remains scarce. One of the reasons for this is conservativeness of Lyapunov conditions. This article proposes a methodology that reduces conservatism of CLF design and is applicable to a wide class of discrete-time nonlinear hybrid systems. Rather than searching for global CLFs off-line, we focus on synthesizing CLFs by solving on-line an optimization problem. This approach makes it possible to derive a trajectory-dependent CLF, which is allowed to be locally non-monotone. Besides the theoretical appeal of the proposed idea, we indicate that for systems affine in control and CLFs based on infinity norms, the corresponding on-line optimization problem can be formulated as a single linear program.
|Title of host publication||Proceedings 12th international conference on Hybrid systems : computation and control, HSCC 2009, April 13-15, 2009, San Francisco, California|
|Editors||R. Majumdar, P. Tabuada|
|Place of Publication||Berlin|
|Number of pages||5|
|Publication status||Published - 2009|
|Name||Lecture Notes in Computer Science|
Lazar, M., & Jokic, A. (2009). Synthesis of trajectory-dependent control Lyapunov functions by a single linear program. In R. Majumdar, & P. Tabuada (Eds.), Proceedings 12th international conference on Hybrid systems : computation and control, HSCC 2009, April 13-15, 2009, San Francisco, California (pp. 237-251). (Lecture Notes in Computer Science; Vol. 5469). Berlin: Springer. https://doi.org/10.1007/978-3-642-00602-9_17