arXiv subjects

Mahendra Singh Tomar

Publications and source records attributed to Mahendra Singh Tomar.

5 recordsLinked to original sources

arXiv2026

Adaptive Model Predictive Control for Ground Vehicles: Review and Demonstrative Implementation

This paper reviews Adaptive Model Predictive Control (AMPC) methods for Autonomous Vehicles (AVs), focusing on control strategies that dynamically adapt to uncertainties and changing conditions in real-time. The critical role of Adaptive Model Predictive Control (AMPC) in addressing the challenges of autonomous vehicle control are discussed. For the scope of this paper, AMPC is defined as a class of Model Predictive Control (MPC) techniques that modify the system model, cost function, constraints, or prediction horizon, based on real-time data. Traditional MPC, while effective for constrained optimization, struggles with model inaccuracies, computational demands, and dynamic environments, necessitating AMPC methods. The review covers existing literature on Gain scheduled MPC, Online Model Estimation MPC, Weight Adaptive MPC, Horizon Adaptive MPC, Learning Based MPC, and Hybrid MPC that combines MPC with other control methods. In addition to the survey, a demonstrative simulation of an adaptive MPC controller is presented that illustrates practical aspects of weight and speed adaptation in trajectory tracking.

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arXiv2022

On a notion of entropy for reachability properties

In this work, we introduce a notion of reachability entropy to characterize the smallest data rate which is sufficient enough to enforce reach-while-stay specification. We also define data rates of coder-controllers that can enforce this specification in finite time. Then, we establish the data-rate theorem which states that the reachability entropy is a tight lower bound of the data rates that allow satisfaction of the reach-while-stay specification. For a system which is related to an another system under feedback refinement relation, we show that the entropy of the former will not be larger than that of the latter. We also provide a procedure to numerically compute an upper bound of the reachability entropy for discrete-time control systems by leveraging their finite abstractions. Finally, we present some examples to demonstrate the effectiveness of the proposed results.

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arXiv2021

Numerical over-approximation of invariance entropy via finite abstractions

For a closed-loop control system with a digital channel between the sensor and the controller, the notion of invariance entropy quantifies the smallest average rate of information above which a given compact subset of the state space can be made invariant. There exist different versions of this quantity for deterministic and uncertain systems, which are equivalent in the deterministic case. In this work, we present algorithms for the numerical computation of these two quantities. In particular, given a subset $Q$ of the state set, we first partition it. Then a controller, in the form of a lookup table that assigns a set of control values to each cell of the partition, is computed to enforce invariance of $Q$. After determinizing the controller, a weighted directed graph is constructed. For deterministic systems, the logarithm of the spectral radius of a transition matrix obtained from the graph gives an upper bound of the entropy. For uncertain systems, the maximum mean cycle weight of the graph upper bounds the entropy. With three deterministic examples, for which the exact value of the invariance entropy is known or can be estimated by other means, we demonstrate that the upper bound obtained by our algorithm is of the same order of magnitude as the actual value. Additionally, our algorithm provides a static coder-controller scheme corresponding to the obtained data-rate bound. Finally, we present the computed upper bounds of invariance entropy for an uncertain linear control system as well.

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arXiv2020

Numerical Estimation of Invariance Entropy for Nonlinear Control Systems

For a closed-loop control system with a digital channel between the sensor and the controller, the notion of invariance entropy quantifies the smallest average rate of information transmission above which a given compact subset of the state space can be made invariant. In this work, we present for the first time an algorithm to numerically compute upper bounds of invariance entropy. With three examples, for which the exact value of the invariance entropy is known to us or can be estimated by other means, we demonstrate that the upper bound obtained by our algorithm is of the same order of magnitude as the actual value. Additionally, our algorithm provides a static coder-controller scheme corresponding to the obtained data-rate bound.

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arXiv2019

Invariance Feedback Entropy of Uncertain Control Systems

We introduce a novel notion of invariance feedback entropy to quantify the state information that is required by any controller that enforces a given subset of the state space to be invariant. We establish a number of elementary properties, e.g. we provide conditions that ensure that the invariance feedback entropy is finite and show for the deterministic case that we recover the well-known notion of entropy for deterministic control systems. We prove the data rate theorem, which shows that the invariance entropy is a tight lower bound of the data rate of any coder-controller that achieves invariance in the closed loop. We analyze uncertain linear control systems and derive a universal lower bound of the invariance feedback entropy. The lower bound depends on the absolute value of the determinant of the system matrix and a ratio involving the volume of the invariant set and the set of uncertainties. Furthermore, we derive a lower bound of the data rate of any static, memoryless coder-controller. Both lower bounds are intimately related and for certain cases it is possible to bound the performance loss due to the restriction to static coder-controllers by $1$ bit/time unit. We provide various examples throughout the paper to illustrate and discuss different definitions and results.

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