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This paper studies the problem of decentralized measurement feedback stabilization of nonlinear interconnected systems. As a natural extension of the recent development on control vector Lyapunov functions, the notion of output control vector Lyapunov function (OCVLF) is introduced for investigating decentralized measurement feedback stabilization problems. Sufficient conditions on (local) stabilizability are discussed which are based on the proposed notion of OCVLF. It is shown that a decentralized controller for a nonlinear interconnected system can be constructed using these conditions under an additional vector dissipation-like condition. To illustrate the proposed method, two examples are given.
We study the new concept of relative coobservability in decentralized supervisory control of discrete-event systems under partial observation. This extends our previous work on relative observability from a centralized setup to a decentralized one. A fundamental concept in decentralized supervisory control is coobservability (and its several variations); this property is not, however, closed under set union, and hence there generally does not exist the supremal element. Our proposed relative coobservability, although stronger than coobservability, is algebraically well-behaved, and the supremal relatively coobservable sublanguage of a given language exists. We present an algorithm to compute this supremal sublanguage. Moreover, relative coobservability is weaker than conormality, which is also closed under set union; unlike conormality, relative coobservability imposes no constraint on disabling unobservable controllable events.
We consider the problem of designing a stabilizing and optimal static controller with a pre-specified sparsity pattern. Since this problem is NP-hard in general, it is necessary to resort to approximation approaches. In this paper, we characterize a class of convex restrictions of this problem that are based on designing a separable quadratic Lyapunov function for the closed-loop system. This approach generalizes previous results based on optimizing over diagonal Lyapunov functions, thus allowing for improved feasibility and performance. Moreover, we suggest a simple procedure to compute favourable structures for the Lyapunov function yielding high-performance distributed controllers. Numerical examples validate our results.
For his work in the economics of climate change, Professor William Nordhaus was a co-recipient of the 2018 Nobel Memorial Prize for Economic Sciences. A core component of the work undertaken by Nordhaus is the Dynamic Integrated model of Climate and Economy, known as the DICE model. The DICE model is a discrete-time model with two control inputs and is primarily used in conjunction with a particular optimal control problem in order to estimate optimal pathways for reducing greenhouse gas emissions. In this paper, we provide a tutorial introduction to the DICE model and we indicate challenges and open problems of potential interest for the systems and control community.
A Lyapunov-based method is presented for stabilizing and controlling of closed quantum systems. The proposed method is constructed upon a novel quantum Lyapunov function of the system state trajectory tracking error. A positive-definite operator in the Lyapunov function provides additional degrees of freedom for the designer. The stabilization process is analyzed regarding two distinct cases for this operator in terms of its vanishing or non-vanishing commutation with the Hamiltonian operator of the undriven quantum system. To cope with the global phase invariance of quantum states as a result of the quantum projective measurement postulate, equivalence classes of quantum states are defined and used in the proposed Lyapunov-based analysis and design. Results show significant improvement in both the set of stabilizable quantum systems and their invariant sets of state trajectories generated by designed control signals. The proposed method can potentially be applied for high-fidelity quantum control purposes in quantum computing frameworks.
This work considers the problem of control and resource scheduling in networked systems. We present DIRA, a Deep reinforcement learning based Iterative Resource Allocation algorithm, which is scalable and control-aware. Our algorithm is tailored towards large-scale problems where control and scheduling need to act jointly to optimize performance. DIRA can be used to schedule general time-domain optimization based controllers. In the present work, we focus on control designs based on suitably adapted linear quadratic regulators. We apply our algorithm to networked systems with correlated fading communication channels. Our simulations show that DIRA scales well to large scheduling problems.