Reachability and Invariance for Linear Sampled–data Systems

IEEE Trans. Automat. Contr.

2024

Ensuring robust constraint satisfaction for an infinite time horizon is a challenging, yet crucial task when deploying safety-critical systems. We address this issue by synthesizing robust control invariant sets for perturbed nonlinear sampled-data systems. This task can be encoded as a nonconvex program for which we propose a tailored, computationally efficient successive convexification algorithm. Based on the zonotopic representation of invariant sets, we obtain an updated candidate for the invariant set and the safety-preserving controller by solving a single convex program. To obtain a possibly large region of safe operation, our algorithm is designed so that the sequence of candidate invariant sets has monotonically increasing volume. We demonstrate the efficacy and scalability of our approach by applying it to a broad range of nonlinear control systems from the literature with up to 20 dimensions.

Section: Solution Conceptmentioning

confidence: 99%

Scalable Computation of Robust Control Invariant Sets of Nonlinear Systems

Schäfer

IEEE Trans. Automat. Contr.

2024

“…2 proceeds in two steps. First, two zonotope sequences are computed that converge to an overapproximation of the discrete-time minimal robust positively invariant (mRPI) set [11]. Second, the zonotope order of this over-approximation is reduced as much as possible while ensuring that the constraints in (11b) and (11c) are satisfied.…”

Section: A Safe Terminal Setmentioning

confidence: 99%

“…We denote these zonotope sequences by Z {0} (•) and Z X (•). Because the feedback matrix K in (10) is stabilizing, Z {0} (•) and Z X (•) would converge to the discretetime mRPI set [11], if no over-approximation of reachable sets to reduce computational complexity was used. To achieve low computation times, we use a simple convergence criterion in line 4 based on the directed Hausdorff distance in (1).…”

Section: Algorithm 2 Safe Terminal Setmentioning

confidence: 99%

“…Inspired by [3], we compute a) safe terminal sets that guarantee robust constraint satisfaction at all times and b) safe initial sets that are as large as possible and can be safely steered into a safe terminal set in finite time. Moreover, we consider systems that are described by sampled-data models [11], where the physical plant evolves in continuous time, whereas the digital controller is implemented in discrete time.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Computing Safe Sets of Linear Sampled-Data Systems

IEEE Control Syst. Lett.

2021

Leveraging autonomous systems in safety-critical applications requires formal robustness guarantees against uncertainties. We address this issue by computing safe terminal sets with corresponding safety-preserving terminal controllers, which ensure robust constraint satisfaction for an infinite time horizon. To maximize the region of operation, we also construct as large as possible safe initial sets that can be safely steered into the safe terminal set in finite time. We use scalable reachability analysis and convex optimization to efficiently compute safe sets of sampled-data systems. These systems are composed of a physical plant evolving in continuous time and a digital controller being implemented in discrete time. We further verify the effectiveness of our robust control approach using a simple double-integrator system and a vehicle-platooning benchmark.

“…First, we compute a small safe terminal set Ω(t k ) containing the origin, which is typically not invariant but can be safely steered into itself in finite time and is closely related to the minimal RPI set [42]. In particular, we determine some finite i k ∈ N >0 so that E(t k+i k ) ⊆ E(t k ) and…”

Section: B Safe Terminal Sets and Controllersmentioning

confidence: 99%

Scalable robust output feedback MPC of linear sampled-data systems

2021 60th IEEE Conference on Decision and Control (CDC)

2021

Cyber-physical control systems typically consist of two components: a clocked digital controller and a physical plant evolving in continuous time. Clearly, the state and input constraints must be satisfied not only at, but also between sampling times of the controller. We address this issue by proposing a robust output feedback model predictive control approach for sampled-data systems, which are affected by additive disturbances and measurement noise. To guarantee robust constraint satisfaction for an infinite time horizon, we present a scalable approach to compute safe terminal sets. Based on these sets and using scalable reachability analysis and convex optimization algorithms, we construct real-time controllers that explicitly consider all online computation times. We demonstrate the usefulness of our robust control approach using a vehicle platooning benchmark from the literature.