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This note studies the global controllability of a general nonlinear system by extending it to affine one. The state space of the obtained affine system admits a nature foliation, each leaf of which is diffeomorphic to the state space of the…
While the optimization landscape of policy gradient methods has been recently investigated for partially observed linear systems in terms of both static output feedback and dynamical controllers, they only provide convergence guarantees to…
We introduce a set of local procedures that are capable of controlling distributed systems that exhibit complex dynamical behavior. These local controllers need only perturb local parameters and use local information about the state of the…
We describe a general strategy for sampling configurations from a given (Gibbs-Boltzmann or other) distribution. It is {\it not} based on the Metropolis concept of establishing a Markov process whose stationary state is the wanted…
A first-principles theory is developed for the general evolution of a key structural characteristic of planar granular systems - the cell order distribution. The dynamic equations are constructed and solved in closed form for a number of…
In the present work, we consider nonlinear control systems for which there exist structural obstacles to the design of classical continuous backstepping feedback laws. We conceive feedback laws such that the origin of the closed-loop system…
This paper gives a summary of a body of work at the intersection of control theory and smooth nonlinear dynamics. The main idea is to transfer the concept of uniform hyperbolicity, central to the theory of smooth dynamical systems, to…
A hallmark of biological intelligence and control is combinatorial generalization: animals are able to learn various things, then piece them together in new combinations to produce appropriate outputs for new tasks. Inspired by the ability…
Ensemble control offers rich and diverse opportunities in mathematical systems theory. In this paper, we present a new paradigm of ensemble control, referred to as distributional control, for ensemble systems. We shift the focus from…
We study a node-wise monotone barrier coupling law, motivated by the synaptic coupling of neural central pattern generators. It is illustrated that this coupling imitates the desirable properties of neural central pattern generators. In…
We introduce and develop the concept of dispersion formation control, bridging a gap between shape-assembly studies in physics and biology and formation control theory. In current formation control studies, the control objectives typically…
In this paper, formation control for reduced attitude is studied, in which both stationary and rotating regular tetrahedron formation can be achieved and are asymptotically stable under a large family of gain functions in the control.…
We introduce a general formalism, based on the stochastic formulation of quantum mechanics, to obtain localized quasi-classical wave packets as dynamically controlled systems, for arbitrary anharmonic potentials. The control is in general…
Nonlinear control allocation is an important part of modern nonlinear dynamic inversion based flight control systems which require highly accurate model of aircraft aerodynamics. Generally, an accurately implemented onboard model determines…
We present a hierarchical model predictive control approach for large-scale systems based on dual decomposition. The proposed scheme allows coupling in both dynamics and constraints between the subsystems and generates a primal feasible…
This paper establishes a unified element-based framework for formation control by introducing the concept of the deformation gradient from continuum mechanics. Unlike traditional methods that rely on geometric constraints defined on graph…
In this paper, we propose a novel and distributed formation control method for autonomous robots to follow the desired formation while tracking a moving target in dynamic environments. In our approach, the desired formations, which include…
Contraction analysis establishes exponential incremental convergence of a nonlinear system by solving a linear matrix inequality for a contraction metric, and has become a standard resource for solving problems in nonlinear control and…
Distributed formation maneuver control refers to the problem of maneuvering a group of agents to change their formation shape by adjusting the motions of partial agents, where the controller of each agent only requires local information…
In this paper, we solve the problem of finding a certified control policy that drives a robot from any given initial state and under any bounded disturbance to the desired reference trajectory, with guarantees on the convergence or bounds…