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Register a new userOver-approximating reachable tubes of linear time-varying systems
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Added by
Gunther Rei{\\ss}ig
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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We present a method to over-approximate reachable tubes over compact time-intervals, for linear continuous-time, time-varying control systems whose initial states and inputs are subject to compact convex uncertainty. The method uses numerical approximations of transition matrices, is convergent of first order, and assumes the ability to compute with compact convex sets in finite dimension. We also present a variant that applies to the case of zonotopic uncertainties, uses only linear algebraic operations, and yields zonotopic over-approximations. The performance of the latter variant is demonstrated on an example.
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We study predictive control in a setting where the dynamics are time-varying and linear, and the costs are time-varying and well-conditioned. At each time step, the controller receives the exact predictions of costs, dynamics, and disturbances for the future $k$ time steps. We show that when the prediction window $k$ is sufficiently large, predictive control is input-to-state stable and achieves a dynamic regret of $O(lambda^k T)$, where $lambda < 1$ is a positive constant. This is the first dynamic regret bound on the predictive control of linear time-varying systems. Under more assumptions on the terminal costs, we also show that predictive control obtains the first competitive bound for the control of linear time-varying systems: $1 + O(lambda^k)$. Our results are derived using a novel proof framework based on a perturbation bound that characterizes how a small change to the system parameters impacts the optimal trajectory.
This paper considers a time-varying optimization problem associated with a network of systems, with each of the systems shared by (and affecting) a number of individuals. The objective is to minimize cost functions associated with the individuals preferences, which are unknown, subject to time-varying constraints that capture physical or operational limits of the network. To this end, the paper develops a distributed online optimization algorithm with concurrent learning of the cost functions. The cost functions are learned on-the-fly based on the users feedback (provided at irregular intervals) by leveraging tools from shape-constrained Gaussian Processes. The online algorithm is based on a primal-dual method, and acts effectively in a closed-loop fashion where: i) users feedback is utilized to estimate the cost, and ii) measurements from the network are utilized in the algorithmic steps to bypass the need for sensing of (unknown) exogenous inputs of the network. The performance of the algorithm is analyzed in terms of dynamic network regret and constraint violation. Numerical examples are presented in the context of real-time optimization of distributed energy resources.
There is an increasing interest in designing differentiators, which converge exactly before a prespecified time regardless of the initial conditions, i.e., which are fixed-time convergent with a predefined Upper Bound of their Settling Time (UBST), due to their ability to solve estimation and control problems with time constraints. However, for the class of signals with a known bound of their $(n+1)$-th time derivative, the existing design methodologies are either only available for first-order differentiators, yielding a very conservative UBST, or result in gains that tend to infinity at the convergence time. Here, we introduce a new methodology based on time-varying gains to design arbitrary-order exact differentiators with a predefined UBST. This UBST is a priori set as one parameter of the algorithm. Our approach guarantees that the UBST can be set arbitrarily tight, and we also provide sufficient conditions to obtain exact convergence while maintaining bounded time-varying gains. Additionally, we provide necessary and sufficient conditions such that our approach yields error dynamics with a uniformly Lyapunov stable equilibrium. Our results show how time-varying gains offer a general and flexible methodology to design algorithms with a predefined UBST.
This paper deals with the stability analysis problem of discrete-time switched linear systems with ranged dwell time. A novel concept called L-switching-cycle is proposed, which contains sequences of multiple activation cycles satisfying the prescribed ranged dwell time constraint. Based on L-switching-cycle, two sufficient conditions are proposed to ensure the global uniform asymptotic stability of discrete-time switched linear systems. It is noted that two conditions are equivalent in stability analysis with the same $L$-switching-cycle. These two sufficient conditions can be viewed as generalizations of the clock-dependent Lyapunov and multiple Lyapunov function methods, respectively. Furthermore, it has been proven that the proposed L-switching-cycle can eventually achieve the nonconservativeness in stability analysis as long as a sufficiently long L-switching-cycle is adopted. A numerical example is provided to illustrate our theoretical results.
In this paper, we develop a system identification algorithm to identify a model for unknown linear quantum systems driven by time-varying coherent states, based on empirical single-shot continuous homodyne measurement data of the systems output. The proposed algorithm identifies a model that satisfies the physical realizability conditions for linear quantum systems, challenging constraints not encountered in classical (non-quantum) linear system identification. Numerical examples on a multiple-input multiple-output optical cavity model are presented to illustrate an application of the identification algorithm.
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