Related papers: Mathematical models for geometric control theory
In this paper a geometric approach to the trajectory tracking control of Unmanned Aerial Vehicles with thrust vectoring capabilities is proposed. The control design is suitable for aerial systems that allow to effectively decouple position…
The ability to control quantum systems using shaped fields as well as to infer the states of such controlled systems from measurement data are key tasks in the design and operation of quantum devices. Here we associate the success of…
Many real-world systems are composed of many individual components that interact with one another in a complex pattern to produce diverse behaviors. Understanding how to intervene in these systems to guide behaviors is critically important…
This thesis investigates optimal trajectory tracking of nonlinear dynamical systems with affine controls. The control task is to enforce the system state to follow a prescribed desired trajectory as closely as possible. The concept of…
Inductive bias refers to restrictions on the hypothesis class that enable a learning method to generalize effectively from limited data. A canonical example in control is linearity, which underpins low sample-complexity guarantees for…
This paper extends sliding-mode control theory to nonlinear systems evolving on smooth manifolds. Building on differential geometric methods, we reformulate Filippov's notion of solutions, characterize well-defined vector fields on quotient…
Geometrical stability theory is a powerful set of model-theoretic tools that can lead to structural results on models of a simple first-order theory. Typical results offer a characterization of the groups definable in a model of the theory.…
This paper presents global tracking strategies for the attitude dynamics of a rigid body. It is well known that global attractivity is prohibited for continuous attitude control systems on the special orthogonal group. Such topological…
Robustness is a basic property of any control system. In the context of linear output regulation, it was proved that embedding an internal model of the exogenous signals is necessary and sufficient to achieve tracking of the desired…
Controllability properties are studied for control-affine systems depending on a parameter and with constrained control values. The uncontrolled systems in dimension two and three are subject to a homoclinic bifurcation. This generates two…
Discrete-time stochastic systems are an essential modelling tool for many engineering systems. We consider stochastic control systems that are evolving over continuous spaces. For this class of models, methods for the formal verification…
Understanding conformational change is crucial for programming and controlling the function of many mechanical systems such as allosteric enzymes and tunable metamaterials. Of particular interest is the relationship between the network…
For controller design for systems on manifolds embedded in Euclidean space, it is convenient to utilize a theory that requires a single global coordinate system on the ambient Euclidean space rather than multiple local charts on the…
In this paper, we investigate morphisms of tautological control systems. Given a tautological control system $\mathfrak{H}$ on the manifold N and a mapping $\Phi: M \to N$, we study existence of tautological control system $\mathfrak{G}$ on…
Studying structural properties of linear dynamical systems through invariant subspaces is one of the key contributions of the geometric approach to system theory. In general, a model of the dynamics is required in order to compute the…
In many contexts, simpler models are preferable to more complex models and the control of this model complexity is the goal for many methods in machine learning such as regularization, hyperparameter tuning and architecture design. In deep…
In a recent paper [Phys. Rev. E 57, p. 1550 (1998)] we demonstrated that the symmetries of the evolution equation and the target state have a profound effect on the selection of the admissible control parameters. In the present paper we…
In this paper, we study under which conditions the trajectories of a mechanical control system can track any curve on the configuration manifold. We focus on systems that can be represented as forced affine connection control systems and we…
In this paper, we present a geometric approach for computing the controlled invariant set of a continuous-time control system. While the problem is well studied for in the ellipsoidal case, this family is quite conservative for constrained…
Finite-state models of control systems were proposed by several researchers as a convenient mechanism to synthesize controllers enforcing complex specifications. Most techniques for the construction of such symbolic models have two main…