Symbolic Self-triggered Control of Continuous-time Non-deterministic Systems without Stability Assumptions for 2-LTL Specifications

Fast Synthesis for Symbolic Self-triggered Control under Right-recursive LTL Specifications

“…As in [11], we require the following assumptions, which basically ensure that we can bound the distance between points evolving according to the system dynamics. Note that this does not imply any stability assumptions on Σ.…”

“…We model the first objective using a fragment of LTL, which we call right-recursive LTL, and which is also an extension of 2-LTL, studied in [11]. Let AP denote the set of atomic propositions, i.e., assertions that can be either true or false at each state x ∈ X .…”

“…Theorem 1 (extended from [11]). If S : FRun(S η,τ, ,µ ) → U τ, ,µ solves the problem of Definition 7, then C S : FRun(Σ) → U τ, ,µ solves the controller synthesis problem of Definition 5.…”

“…It was developed in the symbolic control framework for nonlinear systems without stability assumptions proposed in [6]. Our previous work in [11] extended the concept in [2] to the control of continuous-time non-deterministic nonlinear systems for 2-LTL specifications: a subclass of Linear Temporal Logic (LTL) specifications that is strictly more expressive than reach-avoid. Our control objective is to: 1) control the system to satisfy the given 2-LTL formula and 2) restrict the limit average control-signal length to stay above a given threshold.…”

“…In this work, we extend our self-triggered control methodology proposed in [11] to right-recursive LTL specifications. We add the temporal operator Until, which is a basic operator in LTL but must be treated differently from the other operators in 2-LTL.…”