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This work studies the design of safe control policies for large-scale non-linear systems operating in uncertain environments. In such a case, the robust control framework is a principled approach to safety that aims to maximize the…
Exponential dichotomies play a central role in stability theory for dynamical systems. They allow to split the state space into two subspaces, where all trajectories in one subspace decay whereas all trajectories in the other subspace grow,…
In this paper we consider a class of linear time invariant systems with infinitely many unstable modes. By using the parameterization of all stabilizing controllers, we show that H-infinity controllers for such systems can be computed using…
The stabilization of nonlinear systems under zero-state-detectability assumption or its analogues is considered. The proposed supervisory control provides a finite time practical stabilization of output and it is based on uniting local and…
Many dynamical systems, including thermal, fluid, and multi-agent systems, can be represented as weighted graphs. In this paper we consider whether the unstable states of such systems can be observed from limited discrete-time measurement,…
In this paper, we study graphical conditions for structural controllability and accessibility of drifted bilinear systems over Lie groups. We consider a bilinear control system with drift and controlled terms that evolves over the special…
In this paper we consider distributed adaptive stabilization for uncertain multivariable linear systems with a time-varying diagonal matrix gain. We show that uncertain multivariable linear systems are stabilizable by diagonal matrix high…
The method to design exponentially stable adaptive observers is proposed for linear time-invariant systems parameterized by unknown physical parameters. Unlike existing adaptive solutions, the system state-space matrices A, B are not…
This paper presents a novel robust trajectory optimization method for constrained nonlinear dynamical systems subject to unknown bounded disturbances. In particular, we seek optimal control policies that remain robustly feasible with…
This paper is concerned with the development and use of duality theory for a hidden Markov model (HMM) with white noise observations. The main contribution of this work is to introduce a backward stochastic differential equation (BSDE) as a…
Introductory state-space linear control courses focus on linear, time-invariant systems and spend intense efforts by introducing system realizations that allow the student to grasp fundamental concepts, among which controllability,…
This paper studies a class of complex-valued linear systems whose state evolution dependents on both the state vector and its conjugate. The complex-valued linear system comes from linear dynamical quantum control theory and is also…
This paper develops a connection between the asymptotic stability of nonlinear filters and a notion of observability. We consider a general class of hidden Markov models in continuous time with compact signal state space, and call such a…
Infinite-dimensional control systems with outputs are considered in the Hamiltonian formulation with generalized coordinates. An explicit scheme for constructing a dynamic observer for this class of systems is proposed with arbitrary gain…
We consider the problem of learning a realization of a partially observed dynamical system with linear state transitions and bilinear observations. Under very mild assumptions on the process and measurement noises, we provide a finite time…
This work primarily focuses on an operator inference methodology aimed at constructing low-dimensional dynamical models based on a priori hypotheses about their structure, often informed by established physics or expert insights. Stability…
For a parameter-unknown linear descriptor system, this paper proposes data-driven methods to testify the system's type and controllability and then to stabilize it. First, a data-based condition is developed to identify whether this unknown…
The use of available disturbance predictions within a nominal model predictive control formulation is studied. The main challenge that arises is the loss of recursive feasibility and stability guarantees when a persistent disturbance is…
The concept of observability of linear systems initiated with Kalman in the mid 1950s. Roughly a decade later, the observability of nonlinear systems appeared. By such definitions a system is either observable or not. Continuous measures of…
This paper is devoted to the stabilization of a linear control system $y' = A y + B u$ and its suitable non-linear variants where $(A, \cD(A))$ is an infinitesimal generator of a strongly continuous {\it group} in a Hilbert space $\mH$, and…