The Maximal Positively Invariant Set: Polynomial Setting

This note considers the maximal positively invariant set for polynomial discrete time dynamics subject to constraints specified by a basic semialgebraic set. The note utilizes a relatively direct, but apparently overlooked, fact stating that the related preimage map preserves basic semialgebraic structure. In fact, this property propagates to underlying set--dynamics induced by the associated restricted preimage map in general and to its maximal trajectory in particular. The finite time convergence of the corresponding maximal trajectory to the maximal positively invariant set is verified under reasonably mild conditions. The analysis is complemented with a discussion of computational aspects and a prototype implementation based on existing toolboxes for polynomial optimization

Piecewise semi-ellipsoidal control invariant sets

Computing control invariant sets is paramount in many applications. The families of sets commonly used for computations are ellipsoids and polyhedra. However, searching for a control invariant set over the family of ellipsoids is conservative for systems more complex than unconstrained linear time invariant systems. Moreover, even if the control invariant set may be approximated arbitrarily closely by polyhedra, the complexity of the polyhedra may grow rapidly in certain directions. An attractive generalization of these two families are piecewise semi-ellipsoids. We provide in this paper a convex programming approach for computing control invariant sets of this family.Comment: 7 pages, 3 figures, to be published in IEEE Control Systems Letter

Corrigendum to “the Minkowski–Lyapunov equation for linear dynamics: theoretical foundations” (The Minkowski–Lyapunov equation for linear dynamics: theoretical foundations (2014) 50(8) (2015–2024)

Theorem 1 of Raković and Lazar (2014) accidentally misquotes Theorem 1.7.1 of Schneider (1993). This corrigendum rectifies this misquotation, and it points out that the results developed in Raković and Lazar (2014) are not affected by this misquotation. Since Theorem 1.7.1 of Schneider (1993) is utilized in two places in Raković and Lazar (2014), the corrigendum also clarifies its utilization so as to avoid any ambiguity

Corrigendum to “the Minkowski–Lyapunov equation for linear dynamics:theoretical foundations” (The Minkowski–Lyapunov equation for linear dynamics: theoretical foundations (2014) 50(8) (2015–2024)

\u3cp\u3eTheorem 1 of Raković and Lazar (2014) accidentally misquotes Theorem 1.7.1 of Schneider (1993). This corrigendum rectifies this misquotation, and it points out that the results developed in Raković and Lazar (2014) are not affected by this misquotation. Since Theorem 1.7.1 of Schneider (1993) is utilized in two places in Raković and Lazar (2014), the corrigendum also clarifies its utilization so as to avoid any ambiguity.\u3c/p\u3

Convex model predictive control for collision avoidance

Abstract This manuscript proposes a model predictive control for collision avoidance for the regulation problem of deterministic linear systems, which provides a priori guarantees of strong system theoretic properties, such as positive invariance and asymptotic stability, and high computational efficiency. Notion of safe distance sets is introduced, and also utilized as a novel approach to ensure collision avoidance via suitably defined convex constraints. The proposed convex model predictive control for collision avoidance is obtained by employing interactive strategic‐tactical structure for overall decision‐making. The strategic stage of the overall algorithm employs direct algebraic manipulations in order to construct safe distance sets that ensure collision avoidance. The tactical stage of the overall algorithm employs strictly convex quadratic programs for the optimization of local finite horizon predicted control processes. The dynamically compatible interaction of strategic and tactical stages of the overall algorithm is ensured by construction, which guarantees structural and computational benefits. These novel and unique features effectively enable both real time implementation and real life utilization of model predictive control for collision avoidance

Model Predictive Control in Aerospace Systems: Current State and Opportunities

CONTROLLER design is more troublesome in aerospace systems due to, inter alia, diversity of mission platforms, convoluted nonlinear dynamics, predominantly strict mission and resource constraints, and demands for guaranteed operability within a wide range of operating conditions that can undergo structural or unexpected changes. Most of the space systems (e.g., planetary observers, rovers, space telescopes, spacecraft optical systems, etc.) require studious design, production, and testing processes. Indeed, space systemsare required to endure a wide spectrumof environmental changes with limited resources and are typically subject to partial, highly expensive, or even nonexistent service or repair. Clearly, aerospace missions induce high cost, require long development times as well as long mission lifespan, and demand high-fidelity operation so that, not surprisingly, related control tasks are significantly more demanding in aerospace compared to many other industries.</p