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Suman Chakravorty

Publications and source records attributed to Suman Chakravorty.

At least 37 records · Page 2Linked to original sources
arXiv2024

Convexity in Optimal Control Problems

This paper investigates the central role played by the Hamiltonian in continuous-time nonlinear optimal control problems. We show that the strict convexity of the Hamiltonian in the control variable is a sufficient condition for the existence of a unique optimal trajectory, and the nonlinearity/non-convexity of the dynamics and the cost are immaterial. The analysis is extended to discrete-time problems, revealing that discretization destroys the convex Hamiltonian structure, leading to multiple spurious optima, unless the time discretization is sufficiently small. We present simulated results comparing the "indirect" Iterative Linear Quadratic Regulator (iLQR) and the "direct" Sequential Quadratic Programming (SQP) approach for solving the optimal control problem for the cartpole and pendulum models to validate the theoretical analysis. Results show that the ILQR always converges to the "globally" optimum solution while the SQP approach gets stuck in spurious minima given multiple random initial guesses for a time discretization that is insufficiently small, while both converge to the same unique solution if the discretization is sufficiently small.

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arXiv2024

An Information-State Based Approach to Linear Time Varying System Identification and Control

This paper considers the problem of system identification for linear time varying systems. We propose a new system realization approach that uses an "information-state" as the state vector, where the "information-state" is composed of a finite number of past inputs and outputs. The system identification algorithm uses input-output data to fit an autoregressive moving average model (ARMA) to represent the current output in terms of finite past inputs and outputs. This information-state-based approach allows us to directly realize a state-space model using the estimated time varying ARMA paramters linear time varying (LTV) systems. The paper develops the theoretical foundation for using ARMA parameters-based system representation using only the concept of linear observability, details the reasoning for exact output modeling using only the finite history, and shows that there is no need to separate the free and the forced response for identification. The paper also discusses the implications of using the information-state system for optimal output feedback control and shows that the solution obtained using a suitably posed information state problem is optimal for the original problem. The proposed approach is tested on various different systems, and the performance is compared with state-of-the-art LTV system identification techniques.

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arXiv2024

On the Predictive Capability of Dynamic Mode Decomposition for Nonlinear Periodic Systems with Focus on Orbital Mechanics

This paper discusses the predictive capability of Dynamic Mode Decomposition (DMD) in the context of orbital mechanics. The focus is specifically on the Hankel variant of DMD which uses a stacked set of time-delayed observations for system identification and subsequent prediction. A theory on the minimum number of time delays required for accurate reconstruction of periodic trajectories of nonlinear systems is presented and corroborated using experimental analysis. In addition, the window size for training and prediction regions, respectively, is presented. The need for a meticulous approach while using DMD is emphasized by drawing comparisons between its performance on two candidate satellites, the ISS and MOLNIYA-3-50.

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arXiv2023

Learning to Control under Uncertainty with Data-Based Iterative Linear Quadratic Regulator

This paper studies the learning-to-control problem under process and sensing uncertainties for dynamical systems. In our previous work, we developed a data-based generalization of the iterative linear quadratic regulator (iLQR) to design closed-loop feedback control for high-dimensional dynamical systems with partial state observation. This method required perfect simulation rollouts which are not realistic in real applications. In this work, we briefly introduce this method and explore its efficacy under process and sensing uncertainties. We prove that in the fully observed case where the system dynamics are corrupted with noise but the measurements are perfect, it still converges to the global minimum. However, in the partially observed case where both process and measurement noise exist in the system, this method converges to a biased "optimum". Thus multiple rollouts need to be averaged to retrieve the true optimum. The analysis is verified in two nonlinear robotic examples simulated in the above cases.

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arXiv2023

An Information-state based Approach to the Optimal Output Feedback Control of Nonlinear Systems

This paper develops a data-based approach to the closed-loop output feedback control of nonlinear dynamical systems with a partial nonlinear observation model. We propose an information state based approach to rigorously transform the partially observed problem into a fully observed problem where the information state consists of the past several observations and control inputs. We further show the equivalence of the transformed and the initial partially observed optimal control problems and provide the conditions to solve for the deterministic optimal solution. We develop a data based generalization of the iterative Linear Quadratic Regulator (iLQR) to partially observed systems using a local linear time varying model of the information state dynamics approximated by an Autoregressive moving average (ARMA) model, that is generated using only the input-output data. This open-loop trajectory optimization solution is then used to design a local feedback control law, and the composite law then provides an optimum solution to the partially observed feedback design problem. The efficacy of the developed method is shown by controlling complex high dimensional nonlinear dynamical systems in the presence of model and sensing uncertainty.

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arXiv2023

An Optimal Solution to Infinite Horizon Nonlinear Control Problems

In this paper, we consider the infinite horizon optimal control problem for nonlinear systems. Under the conditions of controllability of the linearized system around the origin, and nonlinear controllability of the system to a terminal set containing the origin, we establish an approximate regularized solution approach consisting of a ``finite free final time" optimal transfer problem to the terminal set, and an infinite horizon linear regulation problem within the terminal set, that is shown to render the origin globally asymptotically stable. Further, we show that the approximations converge to the true optimal cost function as the size of the terminal set decreases to zero. The approach is empirically evaluated on the pendulum and cart-pole swing-up problems to show that the finite time transfer is far shorter than the effective horizon required to solve the infinite horizon problem without the proposed regularization.

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arXiv2022

Optimal Control of Material Micro-Structures

In this paper, we consider the optimal control of material micro-structures. Such material micro-structures are modeled by the so-called phase field model. We study the underlying physical structure of the model and propose a data based approach for its optimal control, along with a comparison to the control using a state of the art Reinforcement Learning (RL) algorithm. Simulation results show the feasibility of optimally controlling such micro-structures to attain desired material properties and complex target micro-structures.

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arXiv2022

On the Search for Feedback in Reinforcement Learning

The problem of Reinforcement Learning (RL) in an unknown nonlinear dynamical system is equivalent to the search for an optimal feedback law utilizing the simulations/ rollouts of the dynamical system. Most RL techniques search over a complex global nonlinear feedback parametrization making them suffer from high training times as well as variance. Instead, we advocate searching over a local feedback representation consisting of an open-loop sequence, and an associated optimal linear feedback law completely determined by the open-loop. We show that this alternate approach results in highly efficient training, the answers obtained are repeatable and hence reliable, and the resulting closed performance is superior to global state-of-the-art RL techniques. Finally, if we replan, whenever required, which is feasible due to the fast and reliable local solution, it allows us to recover global optimality of the resulting feedback law.

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arXiv2021

On the Convergence of Reinforcement Learning in Nonlinear Continuous State Space Problems

We consider the problem of Reinforcement Learning for nonlinear stochastic dynamical systems. We show that in the RL setting, there is an inherent ``Curse of Variance" in addition to Bellman's infamous ``Curse of Dimensionality", in particular, we show that the variance in the solution grows factorial-exponentially in the order of the approximation. A fundamental consequence is that this precludes the search for anything other than ``local" feedback solutions in RL, in order to control the explosive variance growth, and thus, ensure accuracy. We further show that the deterministic optimal control has a perturbation structure, in that the higher order terms do not affect the calculation of lower order terms, which can be utilized in RL to get accurate local solutions.

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arXiv2020

Experiments with Tractable Feedback in Robotic Planning under Uncertainty: Insights over a wide range of noise regimes (Extended Report)

We consider the problem of robotic planning under uncertainty. This problem may be posed as a stochastic optimal control problem, complete solution to which is fundamentally intractable owing to the infamous curse of dimensionality. We report the results of an extensive simulation study in which we have compared two methods, both of which aim to salvage tractability by using alternative, albeit inexact, means for treating feedback. The first is a recently proposed method based on a near-optimal "decoupling principle" for tractable feedback design, wherein a nominal open-loop problem is solved, followed by a linear feedback design around the open-loop. The second is Model Predictive Control (MPC), a widely-employed method that uses repeated re-computation of the nominal open-loop problem during execution to correct for noise, though when interpreted as feedback, this can only said to be an implicit form. We examine a much wider range of noise levels than have been previously reported and empirical evidence suggests that the decoupling method allows for tractable planning over a wide range of uncertainty conditions without unduly sacrificing performance.

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arXiv2020

D2C 2.0: Decoupled Data-Based Approach for Learning to Control Stochastic Nonlinear Systems via Model-Free ILQR

In this paper, we propose a structured linear parameterization of a feedback policy to solve the model-free stochastic optimal control problem. This parametrization is corroborated by a decoupling principle that is shown to be near-optimal under a small noise assumption, both in theory and by empirical analyses. Further, we incorporate a model-free version of the Iterative Linear Quadratic Regulator (ILQR) in a sample-efficient manner into our framework. Simulations on systems over a range of complexities reveal that the resulting algorithm is able to harness the superior second-order convergence properties of ILQR. As a result, it is fast and is scalable to a wide variety of higher dimensional systems. Comparisons are made with a state-of-the-art reinforcement learning algorithm, the Deep Deterministic Policy Gradient (DDPG) technique, in order to demonstrate the significant merits of our approach in terms of training-efficiency.

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arXiv2019

Decoupling stochastic optimal control problems for efficient solution: insights from experiments across a wide range of noise regimes

We consider the problem of robotic planning under uncertainty in this paper. This problem may be posed as a stochastic optimal control problem, a solution to which is fundamentally intractable owing to the infamous "curse of dimensionality". Hence, we consider the extension of a "decoupling principle" that was recently proposed by some of the authors, wherein a nominal open-loop problem is solved followed by a linear feedback design around the open-loop, and which was shown to be near-optimal to second order in terms of a "small noise" parameter, to a much wider range of noise levels. Our empirical evidence suggests that this allows for tractable planning over a wide range of uncertainty conditions without unduly sacrificing performance.

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arXiv2019

Decoupled Data Based Approach for Learning to Control Nonlinear Dynamical Systems

This paper addresses the problem of learning the optimal control policy for a nonlinear stochastic dynamical system with continuous state space, continuous action space and unknown dynamics. This class of problems are typically addressed in stochastic adaptive control and reinforcement learning literature using model-based and model-free approaches respectively. Both methods rely on solving a dynamic programming problem, either directly or indirectly, for finding the optimal closed loop control policy. The inherent `curse of dimensionality' associated with dynamic programming method makes these approaches also computationally difficult. This paper proposes a novel decoupled data-based control (D2C) algorithm that addresses this problem using a decoupled, `open loop - closed loop', approach. First, an open-loop deterministic trajectory optimization problem is solved using a black-box simulation model of the dynamical system. Then, a closed loop control is developed around this open loop trajectory by linearization of the dynamics about this nominal trajectory. By virtue of linearization, a linear quadratic regulator based algorithm can be used for this closed loop control. We show that the performance of D2C algorithm is approximately optimal. Moreover, simulation performance suggests significant reduction in training time compared to other state of the art algorithms.

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arXiv2019

T-PFC: A Trajectory-Optimized Perturbation Feedback Control Approach

Traditional stochastic optimal control methods that attempt to obtain an optimal feedback policy for nonlinear systems are computationally intractable. In this paper, we derive a decoupling principle between the open loop plan, and the closed loop feedback gains, that leads to a perturbation feedback control based solution to optimal control problems under action uncertainty, that is near-optimal to the third order. Extensive numerical simulations validate the theory, revealing a wide range of applicability, coping with medium levels of noise. The performance is compared with Nonlinear Model Predictive Control in several difficult robotic planning and control examples that show near identical performance to NMPC while requiring much lesser computational effort. It also leads us to raise the bigger question as to why NMPC should be used in robotic control as opposed to perturbation feedback approaches.

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arXiv2018

A Decoupled Data Based Approach to Stochastic Optimal Control Problems

This paper studies the stochastic optimal control problem for systems with unknown dynamics. A novel decoupled data based control (D2C) approach is proposed, which solves the problem in a decoupled "open loop-closed loop" fashion that is shown to be near-optimal. First, an open-loop deterministic trajectory optimization problem is solved using a black-box simulation model of the dynamical system using a standard nonlinear programming (NLP) solver. Then a Linear Quadratic Regulator (LQR) controller is designed for the nominal trajectory-dependent linearized system which is learned using input-output experimental data. Computational examples are used to illustrate the performance of the proposed approach with three benchmark problems.

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arXiv2018

SLAP: Simultaneous Localization and Planning Under Uncertainty for Physical Mobile Robots via Dynamic Replanning in Belief Space: Extended version

Simultaneous localization and Planning (SLAP) is a crucial ability for an autonomous robot operating under uncertainty. In its most general form, SLAP induces a continuous POMDP (partially-observable Markov decision process), which needs to be repeatedly solved online. This paper addresses this problem and proposes a dynamic replanning scheme in belief space. The underlying POMDP, which is continuous in state, action, and observation space, is approximated offline via sampling-based methods, but operates in a replanning loop online to admit local improvements to the coarse offline policy. This construct enables the proposed method to combat changing environments and large localization errors, even when the change alters the homotopy class of the optimal trajectory. It further outperforms the state-of-the-art FIRM (Feedback-based Information RoadMap) method by eliminating unnecessary stabilization steps. Applying belief space planning to physical systems brings with it a plethora of challenges. A key focus of this paper is to implement the proposed planner on a physical robot and show the SLAP solution performance under uncertainty, in changing environments and in the presence of large disturbances, such as a kidnapped robot situation.

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arXiv2017

A Separation-based Approach to Data-based Control for Large-Scale Partially Observed Systems

This paper studies the partially observed stochastic optimal control problem for systems with state dynamics governed by partial differential equations (PDEs) that leads to an extremely large problem. First, an open-loop deterministic trajectory optimization problem is solved using a black-box simulation model of the dynamical system. Next, a Linear Quadratic Gaussian (LQG) controller is designed for the nominal trajectory-dependent linearized system which is identified using input-output experimental data consisting of the impulse responses of the optimized nominal system. A computational nonlinear heat example is used to illustrate the performance of the proposed approach.

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