Dipankar Maity

Optimal mission planner with timed temporal logic constraints

In this paper, we present an optimization based method for path planning of a mobile robot subject to time bounded temporal constraints, in a dynamic environment. Temporal logic (TL) can address very complex task specification such as safety, coverage, motion sequencing etc. We use metric temporal logic (MTL) to encode the task specifications with timing constraints. We then translate the MTL formulae into mixed integer linear constraints and solve the associated optimization problem using a mixed integer linear program solver. This approach is different from the automata based methods which generate a finite abstraction of the environment and dynamics, and use an automata theoretic approach to formally generate a path that satisfies the TL specifications. We have applied our approach on several case studies in complex dynamical environments subjected to timed temporal specifications.

Event based control of stochastic linear systems

In this paper, an event based control strategy for linear systems under stochastic disturbances is presented where the control input generator generates a control which tries to mimic a state feedback control between two successive events. The control input is generated in such a way that the error between the state of this system and the continuous state feedback system is bounded. The event generator triggers an event based on this error and the control input generator modifies its control input in such a way that it corroborates that the error generated up to this triggering instance is reduced to zero and thus it does not have any effect on the future states regardless of the stability of the plant. It is also shown that under this event triggering mechanism, the control input generator generates the control in such a way that the error bound could be made arbitrarily small.

Timed automata approach for motion planning using metric interval temporal logic

In this paper, we consider the robot motion (or task) planning problem under some given bounded time high level specifications. We use metric interval temporal logic (MITL), a member of the temporal logic family, to represent the task specification and then we provide a constructive way to generate a timed automaton and methods to look for accepting runs on the automaton to find a feasible motion (or path) sequence for the robot to complete the task.

Motion planning in dynamic environments with bounded time temporal logic specifications

In this paper, we consider the problem of robotic motion planning that satisfies some bounded time high level specifications. Although temporal logic can efficiently express high level specifications such as coverage, obstacle avoidance, temporal ordering of tasks etc., it fails to address problems with explicit timing constraints. The inherent limitations of Linear Temporal Logic (LTL) to address problems with explicit timing constraints have been overcome by translating the planning problem from the workspace of the robot to a higher dimensional space called spacetime where the existing LTL semantics and grammar are sufficient to mathematically formulate the bounded time high level specifications. A discrete path will be generated, that will meet the specifications with all timing constraints and, at the same time, it will optimize some cost function. A continuous trajectory satisfying the continuous dynamics of the robot will be generated from the discrete path using proper control laws.

Event based control for control affine nonlinear systems: A Lyapunov function based approach

In this paper, we propose an event based control strategy for control affine nonlinear systems. The proposed method ensures sufficient reduction in communication by only invoking a communication when some event has occurred. The error between the continuous state feedback nonlinear system and the event based system can be bounded in an invariant set. The upper bound of this error is derived which can be controlled by appropriately choosing the parameters for the event triggering function. This method is then applied to a networked nonlinear system of inverted pendulum and a non-linearizable nonlinear system.

Strategies for two-player differential games with costly information

In this work, a two players nonzero-sum differential game is considered, where one player tries to minimize some predefined cost and the other tries to maximize the same. The game is described by a stochastic differential system and the actions of the players serve as the control inputs to the dynamical system. The cost being a function of the actions chosen by the players and the state of the dynamical system, the players aim to control the state in order to optimize the cost functional. However in this problem the players do not have the access to the states for every time, rather the states are available at discrete time instances after some finite costs are paid by the players. The inclusion of the information-cost makes the structure of the cost functional non-classical. The work presents the strategies for the players under no-cost information access as well as under costly information access. Explicit time instances for the information access are also derived by solving certain finite dimensional optimization problems.

Optimal strategies for stochastic linear quadratic differential games with costly information

A two players stochastic differential game is considered with a given cost function. The players engage in a non-cooperative game where one tries to minimize and the other tries to maximize the cost. The players are given a dynamical system and their actions serve as the control inputs to the dynamical system. Their job is to control the state of this dynamical system to optimize the given objective function. We use the term “state of the game” to describe the state of this dynamical system. The challenge is that none of the players has access to the state of the game for all time, rather they can access the state intermittently and only after paying some information cost. Thus the cost structure is non-classical for a linear-quadratic game and it incorporates the value of information. We provide the Nash equilibrium strategy for the players under full state information access at no cost, as well as under costly state information access. The optimal instances for accessing the state information are also explicitly computed for the players.

Stochastic differential linear-quadratic games with intermittent asymmetric observations

In this paper, we consider a two-players stochastic linear quadratic game framework. The game is partially observed and each player has their own private observation. The challenge is that none of the players has access to the continuum observations, rather they can access their respective observations at discrete time instances by operating a switch unanimously. The operation of the switch is costly and hence the gathering of the observations are costly. Each player is equipped with finite memory and she can only use the latest observation to construct the control strategy. The private observations of the players lead to a source of asymmetry in this game. Moreover, the players have different costs for operating the switch, which is another source of asymmetry. We study the structural properties of the Nash equilibrium for this particular class of problems and then we finally show that the switching problem simplifies to a bi-objective optimization problem.

Asymptotic policies for stochastic differential linear quadratic games with intermittent state feedback

In this paper, we consider infinite horizon linear quadratic stochastic differential games where the games are neither open-loop nor closed-loop. The state of the game dynamics is measured only when a certain switch is closed. The switch requires unanimous operation by the players, and continuum state measurements are not possible. There is an upper bound on the number of times the switch can be closed. Each player is given a quadratic cost function and the objective of each player is to design a switching strategy and a control strategy in order to optimize their respective cost function. We investigate the Nash control strategy and optimal switching policy for this game with two different cost structures: discounted cost and average-time cost.

The effect of delays in the Economic Dispatch Problem for smart grid architectures

We consider the Economic Dispatch Problem (EDP) in power systems for a smart-grid friendly environment. We develop a consensus based decentralized optimization algorithm that evolves in a time-varying communication network that suffers from multiple propagation time-dependent delays. This paper, being an improvisation of an earlier work of ours, addresses the effects of time dependent delays in a fully decentralized network. We show analytically and by simulation that propagation delays may not only affect the performance of the dynamic algorithm that solves the EDP but can also destabilize the system.