Time-Varying Sensor and Actuator Selection for Uncertain Cyber-Physical Systems

Abstract

We propose methods to solve time-varying, sensor and actuator (SaA) selection problems for uncertain cyberphysical systems. We show that many SaA selection problems for optimizing a variety of control and estimation metrics can be posed as semidefinite optimization problems with mixed-integer bilinear matrix inequalities (MIBMIs). Although this class of optimization problems are computationally challenging, we present tractable approaches that directly tackle MIBMIs, providing both upper and lower bounds, and that lead to effective heuristics for SaA selection. The upper and lower bounds are obtained via successive convex approximations and semidefinite programming relaxations, respectively, and selections are obtained with a novel slicing algorithm from the solutions of the bounding problems. Custom branch-and-bound and combinatorial greedy approaches are also developed for a broad class of systems for comparison. Finally, comprehensive numerical experiments are performed to compare the different methods and illustrate their effectiveness.Index Terms-Sensor and actuator selection, cyber-physical systems, linear matrix inequalities, controller design, observer design, mixed integer programming.

Sensor Placement Strategies for Some Classes of Nonlinear Dynamic Systems via Lyapunov Theory

“…and u based on f I i (·) 3 set:S as a subset in C with the greatest upper bound 4 Phase I: find the best upper bound 5 while u − l > h and S > x do 6 SplitS via BnB routines 7 Update C,S, l, and u based on f I i (·) 8 Phase II: find the best lower bound 9 while u − l > h and ∃S j ∈ C, |S j | > x do 10 Split S j via BnB routines 11 Update C,S, l, and u based on f I i (·) 12 Output: β i ← u not contain any maximizer is then discarded. These two routines are performed iteratively until the algorithm terminates.…”

“…To solve P2, one reasonable approach is to transform P2 into MISDP. The reformulation of P2 from nonconvex MISDP to convex MISDP can be carried out by either using big-M method [7], [24] or McCormick's relaxation [6], [25]. With that in mind, here we present a way of reformulating P2 into MISDP via McCormick's relaxation.…”

“…For instance, if the 0/1 integer constraint is relaxed such that γ j ∈ [0, 1], P2 can be solved through SDP routines-our earlier work [7] presents a thorough study on addressing actuator selection for linear dynamic systems through a robust control framework via SDP relaxations and approximations, as well as big-M method and heuristics. Recently, [9] revisits the problem described in [7] by proposing an approach that combines a new reformulation method to tackle the nonconvexity due to the multiplication between integer variables and matrix variable with BnB algorithm. By limiting the number of iterations on the BnB algorithm, the computational time can be shortened.…”

Optimal linear combination of sensors and actuators to enforce an interior conic open‐loop system

“…Control allocation is often necessary in redundantly actuated systems, such as parallel manipulators or fault‐tolerant systems, where the dimension of the control signal is less than or equal to the number of actuators available . Furthermore, a system's sensors and actuators can simultaneously be combined or selected in an optimal manner to minimize closed‐loop performance metrics or the number of sensors and actuators needed for closed‐loop stability …”

“…29 Control allocation is often necessary in redundantly actuated systems, such as parallel manipulators or fault-tolerant systems, where the dimension of the control signal is less than or equal to the number of actuators available. 30,31 Furthermore, a system's sensors and actuators can simultaneously be combined or selected in an optimal manner to minimize closed-loop performance metrics 32,33 or the number of sensors and actuators needed for closed-loop stability. 34 The novel contributions of this paper include techniques to linearly combine an LTI system's actuators and/or sensors in such a manner that the new system is interior conic with prescribed bounds and the difference between the new system and a specified desired system is minimized in a weighted  2 or  ∞ sense.…”