arXiv subjects

Siddharth H. Nair

Publications and source records attributed to Siddharth H. Nair.

At least 19 recordsLinked to original sources

arXiv2026

SHIELD: Scalable Optimal Control with Certification using Duality and Convexity

We present SHIELD, a hierarchical algorithm that reduces both the decision-variable dimension and the constraint set in $\ell_1$-regularized convex programs. From strong convexity and Lagrangian duality, we derive certificates that \emph{safely} discard constraints and decision variables while guaranteeing that all removed constraints remain satisfied and all removed variables are null. To further accelerate the proposed algorithm, we propose a transformer-based deep neural network to guide the dual certificate inference. We validate SHIELD on stochastic model predictive control (SMPC) in complex, multi-modal traffic scenarios, comparing against a full-dimensional SMPC policy. Numerical simulations demonstrate order-of-magnitude computational speedups while preserving feasibility and closed-loop safety, highlighting the practicality of certifiably safe, lightweight MPC in complex driving scenes.

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arXiv2025

Scalable Multi-modal Model Predictive Control via Duality-based Interaction Predictions

We propose a hierarchical architecture designed for scalable real-time Model Predictive Control (MPC) in complex, multi-modal traffic scenarios. This architecture comprises two key components: 1) RAID-Net, a novel attention-based Recurrent Neural Network that predicts relevant interactions along the MPC prediction horizon between the autonomous vehicle and the surrounding vehicles using Lagrangian duality, and 2) a reduced Stochastic MPC problem that eliminates irrelevant collision avoidance constraints, enhancing computational efficiency. Our approach is demonstrated in a simulated traffic intersection with interactive surrounding vehicles, showcasing a 12x speed-up in solving the motion planning problem. A video demonstrating the proposed architecture in multiple complex traffic scenarios can be found here: https://youtu.be/-pRiOnPb9_c. GitHub: https://github.com/MPC-Berkeley/hmpc_raidnet

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arXiv2024

Multi-Objective Learning Model Predictive Control

Multi-Objective Learning Model Predictive Control is a novel data-driven control scheme which improves a linear system's closed-loop performance with respect to several convex control objectives over iterations of a repeated task. At each task iteration, collected system data is used to construct terminal components of a Model Predictive Controller. The formulation presented in this paper ensures that closed-loop control performance improves between successive iterations with respect to each objective. We provide proofs of recursive feasibility and performance improvement, and show that the converged policy is Pareto optimal. Simulation results demonstrate the applicability of the proposed approach.

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arXiv2023

Predictive Control for Autonomous Driving with Uncertain, Multi-modal Predictions

We propose a Stochastic MPC (SMPC) formulation for path planning with autonomous vehicles in scenarios involving multiple agents with multi-modal predictions. The multi-modal predictions capture the uncertainty of urban driving in distinct modes/maneuvers (e.g., yield, keep speed) and driving trajectories (e.g., speed, turning radius), which are incorporated for multi-modal collision avoidance chance constraints for path planning. In the presence of multi-modal uncertainties, it is challenging to reliably compute feasible path planning solutions at real-time frequencies ($\geq$ 10 Hz). Our main technological contribution is a convex SMPC formulation that simultaneously (1) optimizes over parameterized feedback policies and (2) allocates risk levels for each mode of the prediction. The use of feedback policies and risk allocation enhances the feasibility and performance of the SMPC formulation against multi-modal predictions with large uncertainty. We evaluate our approach via simulations and road experiments with a full-scale vehicle interacting in closed-loop with virtual vehicles. We consider distinct, multi-modal driving scenarios: 1) Negotiating a traffic light and a fast, tailgating agent, 2) Executing an unprotected left turn at a traffic intersection, and 3) Changing lanes in the presence of multiple agents. For all of these scenarios, our approach reliably computes multi-modal solutions to the path-planning problem at real-time frequencies.

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arXiv2023

Learning for Online Mixed-Integer Model Predictive Control with Parametric Optimality Certificates

We propose a supervised learning framework for computing solutions of multi-parametric Mixed Integer Linear Programs (MILPs) that arise in Model Predictive Control. Our approach also quantifies sub-optimality for the computed solutions. Inspired by Branch-and-Bound techniques, the key idea is to train a Neural Network/Random Forest, which for a given parameter, predicts a strategy consisting of (1) a set of Linear Programs (LPs) such that their feasible sets form a partition of the feasible set of the MILP and (2) a candidate integer solution. For control computation and sub-optimality quantification, we solve a set of LPs online in parallel. We demonstrate our approach for a motion planning example and compare against various commercial and open-source mixed-integer programming solvers.

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arXiv2023

Robust Output-Lifted Learning Model Predictive Control

We propose an iterative approach for designing Robust Learning Model Predictive Control (LMPC) policies for a class of nonlinear systems with additive, unmodelled dynamics. The nominal dynamics are assumed to be difference flat, i.e., the state and input can be reconstructed using flat output sequences. For the considered class of systems, we synthesize Robust MPC policies and show how to use historical trajectory data collected during iterative tasks to 1) obtain bounds on the unmodelled dynamics and 2) construct a convex value function approximation along with a convex safe set in the space of output sequences for designing terminal components in the Robust MPC design. We show that the proposed strategy guarantees robust constraint satisfaction, asymptotic convergence to a desired subset of the state space, and non-decreasing closed-loop performance at each policy update. Finally, simulation results demonstrate the effectiveness of the proposed strategy on a minimum time control problem using a constrained nonlinear and uncertain vehicle model.

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arXiv2023

Control of Uncertain PWA Systems using Difference-of-Convex Decompositions

In this report, we analyze and design feedback policies for discrete-time Piecewise-Affine (PWA) systems with uncertainty in both the affine dynamics and the polytopic partition. The main idea is to utilise the Difference-of-Convex (DC) decomposition of continuous PWA systems to derive quadratic Lyapunov functions as stability certificates and stabilizing affine policies in a higher dimensional space. When projected back to the state space, we obtain time-varying PWQ Lyapunov functions and time-varying PWA feedback policies.

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arXiv2023

Interaction and Decision Making-aware Motion Planning using Branch Model Predictive Control

Motion planning for autonomous vehicles sharing the road with human drivers remains challenging. The difficulty arises from three challenging aspects: human drivers are 1) multi-modal, 2) interacting with the autonomous vehicle, and 3) actively making decisions based on the current state of the traffic scene. We propose a motion planning framework based on Branch Model Predictive Control to deal with these challenges. The multi-modality is addressed by considering multiple future outcomes associated with different decisions taken by the human driver. The interactive nature of humans is considered by modeling them as reactive agents impacted by the actions of the autonomous vehicle. Finally, we consider a model developed in human neuroscience studies as a possible way of encoding the decision making process of human drivers. We present simulation results in various scenarios, showing the advantages of the proposed method and its ability to plan assertive maneuvers that convey intent to humans.

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arXiv2022

An Invariant Set Approach for Optimization on Integrable Manifolds

Recent results in control systems and numerical integration literature utilize invariant set theory to lift dynamical systems evolving on nonlinear manifolds to those evolving on vector spaces. We leverage this technique to propose an algorithm to solve a class of constrained optimization problems as unconstrained problems.

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arXiv2022

Stochastic MPC with Dual Control for Autonomous Driving with Multi-Modal Interaction-Aware Predictions

We propose a Stochastic MPC (SMPC) approach for autonomous driving which incorporates multi-modal, interaction-aware predictions of surrounding vehicles. For each mode, vehicle motion predictions are obtained by a control model described using a basis of fixed features with unknown weights. The proposed SMPC formulation finds optimal controls which serves two purposes: 1) reducing conservatism of the SMPC by optimizing over parameterized control laws and 2) prediction and estimation of feature weights used in interaction-aware modeling using Kalman filtering. The proposed approach is demonstrated on a longitudinal control example, with uncertainties in predictions of the autonomous and surrounding vehicles.

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arXiv2022

Collision Avoidance for Dynamic Obstacles with Uncertain Predictions using Model Predictive Control

We propose a Model Predictive Control (MPC) for collision avoidance between an autonomous agent and dynamic obstacles with uncertain predictions. The collision avoidance constraints are imposed by enforcing positive distance between convex sets representing the agent and the obstacles, and tractably reformulating them using Lagrange duality. This approach allows for smooth collision avoidance constraints even for polytopes, which otherwise require mixed-integer or non-smooth constraints. We consider three widely used descriptions of the uncertain obstacle position: 1) Arbitrary distribution with polytopic support, 2) Gaussian distributions and 3) Arbitrary distribution with first two moments known. For each case we obtain deterministic reformulations of the collision avoidance constraints. The proposed MPC formulation optimizes over feedback policies to reduce conservatism in satisfying the collision avoidance constraints. The proposed approach is validated using simulations of traffic intersections in CARLA.

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arXiv2022

Stochastic MPC with Multi-modal Predictions for Traffic Intersections

We propose a Stochastic MPC (SMPC) formulation for autonomous driving at traffic intersections which incorporates multi-modal predictions of surrounding vehicles for collision avoidance constraints. The multi-modal predictions are obtained with Gaussian Mixture Models (GMM) and constraints are formulated as chance-constraints. Our main theoretical contribution is a SMPC formulation that optimizes over a novel feedback policy class designed to exploit additional structure in the GMM predictions, and that is amenable to convex programming. The use of feedback policies for prediction is motivated by the need for reduced conservatism in handling multi-modal predictions of the surrounding vehicles, especially prevalent in traffic intersection scenarios. We evaluate our algorithm along axes of mobility, comfort, conservatism and computational efficiency at a simulated intersection in CARLA. Our simulations use a kinematic bicycle model and multimodal predictions trained on a subset of the Lyft Level 5 prediction dataset. To demonstrate the impact of optimizing over feedback policies, we compare our algorithm with two SMPC baselines that handle multi-modal collision avoidance chance constraints by optimizing over open-loop sequences.

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arXiv2021

Output-Lifted Learning Model Predictive Control

We propose a computationally efficient Learning Model Predictive Control (LMPC) scheme for constrained optimal control of a class of nonlinear systems where the state and input can be reconstructed using lifted outputs. For the considered class of systems, we show how to use historical trajectory data collected during iterative tasks to construct a convex value function approximation along with a convex safe set in a lifted space of virtual outputs. These constructions are iteratively updated with historical data and used to synthesize predictive control policies. We show that the proposed strategy guarantees recursive constraint satisfaction, asymptotic stability and non-decreasing closed-loop performance at each policy update. Finally, simulation results demonstrate the effectiveness of the proposed strategy on a piecewise affine (PWA) system, kinematic unicycle and bilinear DC motor.

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arXiv2020

A Semi-Definite Programming Approach to Robust Adaptive MPC under State Dependent Uncertainty

We propose an Adaptive MPC framework for uncertain linear systems to achieve robust satisfaction of state and input constraints. The uncertainty in the system is assumed additive, state dependent, and globally Lipschitz with a known Lipschitz constant. We use a non-parametric technique for online identification of the system uncertainty by approximating its graph via envelopes defined by quadratic constraints. At any given time, by solving a set of convex optimization problems, the MPC controller guarantees robust constraint satisfaction for the closed loop system for all possible values of system uncertainty modeled by the envelope. The uncertainty envelope is refined with data using Set Membership Methods. We highlight the efficacy of the proposed framework via a detailed numerical example.

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arXiv2019

Modeling of Dynamical Systems via Successive Graph Approximations

In this work, we propose a non-parametric technique for online modeling of systems with unknown nonlinear Lipschitz dynamics. The key idea is to successively utilize measurements to approximate the graph of the state-update function using envelopes described by quadratic constraints. The proposed approach is then demonstrated on two control applications: (i) computation of tractable bounds for unmodeled dynamics, and (ii) computation of positive invariant sets. We further highlight the efficacy of the proposed approach via a detailed numerical example.

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arXiv2019

Predictive Control for Chasing a Ground Vehicle using a UAV

We propose a high-level planner for a multirotor to chase a ground vehicle, while simultaneously respecting various state and input constraints. Assuming a minimal kinematic model for the ground vehicle, we use data collected online to generate predictions for our planner within a model predictive control framework. Our solution is demonstrated, both via simulations and experiments on a stable quadcopter platform.

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arXiv2018

Discrete Optimal Control of Interconnected Mechanical Systems

This article develops variational integrators for a class of underactuated mechanical systems using the theory of discrete mechanics. Further, a discrete optimal control problem is formulated for the considered class of systems and subsequently solved using variational principles again, to obtain necessary conditions that characterize optimal trajectories. The proposed approach is demonstrated on benchmark underactuated systems and accompanied by numerical simulations.

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arXiv2018

Control Synthesis for an Underactuated Cable Suspended System Using Dynamic Decoupling

This article studies the dynamics and control of a novel underactuated system, wherein a plate suspended by cables and with a freely moving mass on top, whose other ends are attached to three quadrotors, is sought to be horizontally stabilized at a certain height, with the ball positioned at the center of mass of the plate. The freely moving mass introduces a 2-degree of underactuation into the system. The design proceeds through a decoupling of the quadrotors and the plate dynamics. Through a partial feedback linearization approach, the attitude of the plate and the translational height of the plate is initially controlled, while maintaining a bounded velocity along the $y$ and $x$ directions. These inputs are then synthesized through the quadrotors with a backstepping and timescale separation argument based on Tikhonov's theorem.

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