Ali Pakniyat

A distributed adaptive control strategy is developed for heterogeneous multi-agent systems in nonlinear Brunovsky form with p-dimensional n-order dynamics, operating under time-triggered switching communication topologies.The approach integrates bounded proximity-dependent repulsive potential functions for agent-agent, agent-leader, and agent-obstacle proximity management with neural-network estimators for compensating system uncertainties and disturbances. The resulting distributed control and adaptive laws, together with dwell-time requirements for topology transitions, achieve leader-following consensus. This integrated design provides synchronized formation and robust disturbance rejection in evolving network configurations, and its effectiveness is demonstrated through multiple numerical simulations.

This paper presents a distributed adaptive control strategy for multi-agent systems with heterogeneous dynamics and collision avoidance. We propose an adaptive control strategy designed to ensure leader-following formation consensus while effectively managing collision and obstacle avoidance using potential functions. By integrating neural network-based disturbance estimation and adaptive tuning laws, the proposed strategy ensures consensus and stability in leader-following formations under fixed topologies.

We propose a new method for the numerical solution of the forward–backward stochastic differential equations (FBSDE) appearing in the Feynman-Kac representation of the value function in stochastic optimal control problems. Using Girsanov's change of probability measures, it is demonstrated how a McKean-Markov branched sampling method can be utilized for the forward integration pass, as long as the controlled drift term is appropriately compensated in the backward integration pass. Subsequently, a numerical approximation of the value function is proposed by solving a series of function approximation problems backwards in time along the edges of a space-filling tree consisting of trajectory samples. Moreover, a local entropy-weighted least squares Monte Carlo (LSMC) method is developed to concentrate function approximation accuracy in regions most likely to be visited by optimally controlled trajectories. The proposed methodology is numerically demonstrated for linear and nonlinear stochastic optimal control problems with nonquadratic running costs, which reveal significant convergence improvements over previous FBSDE-based numerical solution methods.

This paper studies the combined maneuver of flying and sailing for a robotic system which is referred to as a flying+sailing drone. Due to the emergence of hybrid systems behavior in tasks which involve both the flying and sailing modes, a hybrid systems formulation of the robotic system is presented. Key characteristics of the system are (i) changes in the dimension of the state space as the system switches from flying to sailing and vice versa and (ii) the presence of autonomous switchings triggered only upon the landing of the drone on the water surface. For the scenario in which the drone’s initial state is given in the flying mode and a fixed terminal state is specified in the sailing mode, the associated optimal control problems are studied within the vertical plane passing through the given points, hence the dynamics of the drone in the flying mode are represented in a five-dimensional state space (associated with three degrees-of-freedom) and in a three-dimensional state space in the sailing mode (associated with two degrees-of-freedom). In particular, the optimal control problems for the minimization of time and the minimization of the control effort are formulated, the associated necessary optimality conditions are obtained from the hybrid minimum principle (HMP), and the associated numerical simulations are presented.

We propose a new method for the numerical solution of the forward-backward stochastic differential equations (FBSDE) appearing in the Feynman-Kac representation of the value function in stochastic optimal control problems. Using Girsanov's change of probability measures, it is demonstrated how a McKean-Markov branched sampling method can be utilized for the forward integration pass, as long as the controlled drift term is appropriately compensated in the backward integration pass. Subsequently, a numerical approximation of the value function is proposed by solving a series of function approximation problems backwards in time along the edges of a space-filling tree consisting of trajectory samples. Moreover, a local entropy-weighted least squares Monte Carlo (LSMC) method is developed to concentrate function approximation accuracy in regions most likely to be visited by optimally controlled trajectories. The proposed methodology is numerically demonstrated on linear and nonlinear stochastic optimal control problems with non-quadratic running costs, which reveal significant convergence improvements over previous FBSDE-based numerical solution methods.

In order to optimally assign a desired probability distribution to the state of a nonlinear stochastic system, a convex duality approach is proposed to arrive at the associated optimality conditions. For a general class of stochastic systems governed by controlled Itô differential equations and subject to constraints on the probability distribution of the state at a fixed terminal time, a measure theoretic formulation is presented and it is shown that the original problem is embedded in a convex linear program on the space of Radon measures and that the embedding is tight, i.e., the optimal solution of both the original and the convex relaxation problems are equal. By exploiting the duality relationship between the space of continuous functions and that of measures, the associated optimality conditions are identified in the form of Hamilton-Jacobi problems where the optimization objective, in addition to the value function evaluation at the initial conditions, includes an extra term which is the integral of the product of the value function at the terminal time and the desired probability distribution. Numerical examples are provided to illustrate the results.