arXiv subjects

Mohammadreza Kamaldar

Publications and source records attributed to Mohammadreza Kamaldar.

8 recordsLinked to original sources

arXiv2026

Composite Adaptive Control Barrier Functions for Safety-Critical Systems with Parametric Uncertainty

Control barrier functions guarantee safety but require accurate system models; parametric uncertainty invalidates these guarantees. Existing robust methods maintain safety via worst-case bounds at the cost of performance, while modular learning schemes decouple estimation from safety and risk constraint violations during transients. This paper presents the composite adaptive control barrier function (CaCBF) algorithm for nonlinear control-affine systems with linear parametric uncertainty. The adaptation law is derived from a composite energy function integrating a logarithmic safety barrier, a control Lyapunov function, and a parameter-error term, creating a direct coupling between estimation accuracy and the safety margin. We prove three main results: (i) the safe set is forward invariant for all bounded parameters, without requiring persistence of excitation; (ii) the safety guarantee is robust to bounded errors in the state-derivative measurement; and (iii) all closed-loop signals are uniformly ultimately bounded. We further prove that the CaCBF admissible control set always contains the robust counterpart as a subset. Simulations of adaptive cruise control, an omnidirectional robot, and a planar drone traversing a narrow gate confirm that CaCBF recovers the performance margin surrendered by robust methods while maintaining strict safety throughout.

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arXiv2026

Extracting Exact Lie Derivatives Without Backpropagation: A Dual Compiler for Neural Control Barrier Functions

A safety filter based on a neural control barrier function (CBF) deployed in an embedded control loop evaluates, at each control cycle, the trained network and its Lie derivatives along the system vector fields, under the memory and worst-case execution time (WCET) constraints that safety-oriented coding standards impose. Reverse-mode automatic differentiation, by which training frameworks obtain these derivatives, retains an activation cache whose size grows with the sum of the layer widths, and general-purpose differentiation runtimes allocate the computational graph from the heap at each call. This paper presents a compiler that evaluates a neural CBF and its exact Lie derivatives by forward-mode dual-number arithmetic. The compiler emits self-contained C++ code in which a single forward pass, without backpropagation, returns the barrier value and its exact Lie derivative along a given vector field; the drift and input Lie derivatives of the safety constraint are obtained from one such pass per vector field, and a second-order extension based on hyper-dual numbers returns the exact second-order Lie derivatives required by CBFs of relative degree two. The dual forward pass requires a workspace bounded by four times the widest layer, independent of network depth, and the emitted code contains no allocation call sites, so the absence of dynamic allocation is verifiable by inspection of the code. On an ESP32-S3 microcontroller, the compiled filter assembles the complete safety constraint in under one millisecond from statically allocated buffers of at most 768 bytes, and the maximum execution time over 1000 evaluations lies within 5% of the median in all three examples, whereas a heap-allocating reverse-mode baseline shows maxima 33% and 70% above its median in the two first-order examples. The compiler and the embedded experiments are released as open-source software.

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arXiv2026

Nonlinear Moving-Horizon Estimation Using State- and Control-Dependent Models

This paper presents a state- and control-dependent moving-horizon estimation (SCD-MHE) algorithm for nonlinear discrete-time systems. The nonlinear dynamics and measurement maps are written exactly in pseudo-linear form using state- and control-dependent coefficient (SCDC) matrices. At each time step, the moving-horizon estimation problem is solved by a sequence of sparse quadratic programs, where the SCDC matrices are refrozen along the trajectory computed by the preceding iteration; the estimator requires no Jacobians and retains the nonlinear model exactly. We show that each quadratic program has a unique solution, characterize the fixed points of the iteration, establish geometric convergence under a contraction condition, and prove that the estimation error of the computed estimate is uniformly bounded under uniform observability, bounded disturbances, a bounded arrival-cost error, and iterates confined to a compact set, for all finite iteration counts. In a quadrotor benchmark with a saturating rangefinder, the altitude RMSE of SCD-MHE is 18 times smaller than that of a nonlinear moving-horizon estimator that solves the nonlinear program and 58 times smaller than that of the extended and unscented Kalman filters, and its per-step computation time is 34 times smaller than that of the nonlinear estimator.

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arXiv2026

Deterministic Non-Smooth Safety via Dual-Algebraic Control Barrier Functions

This paper presents a dual-algebraic framework for control barrier functions (CBFs) that guarantees deterministic execution using exclusively elementary arithmetic. We develop this deterministic approach to solve a fundamental bottleneck in safety-critical control: pointwise minima compose intersecting safe sets, but generate non-smooth boundaries where standard Lie derivatives fail. Existing mathematical workarounds inject approximation bias, probabilistic non-determinism, or combinatorial execution delays that impede hard real-time hardware certification. By embedding the system state and vector field into the dual-number ring, our method extracts both the composite barrier value and its exact directional derivative in a single evaluation. The standard floating-point minimum deterministically isolates a single vertex of the Clarke generalized gradient for the quadratic-program solver. We prove this selected vertex constitutes a Clarke subgradient and the resulting simultaneous-enforcement safety filter guarantees forward invariance. The arithmetic overhead remains a fixed constant factor, independent of state dimension and constraint count. We extend this framework to finite $\min$/$\max$ Boolean compositions, for which enforcement of the routed constraint of each $δ$-active clause guarantees forward invariance, and to systems of higher relative degree, for which a bivariate truncated-dual evaluation extracts the control coupling without symbolic differentiation. Three numerical examples illustrate the computational scaling.

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arXiv2026

Iterative State- and Control-Dependent Model Predictive Control: A Jacobian-Free Formulation for Constrained Nonlinear Systems

This paper presents an iterative model predictive control algorithm that stabilizes constrained nonlinear systems without evaluating a single plant derivative. By factoring the exact nonlinear dynamics into a pseudo-linear form using state- and control-dependent coefficients (SCDCs), we replace the standard nonconvex optimization with a sequence of constrained linear-quadratic programs. Refreezing the coefficient matrices along the previously predicted trajectory drives the iteration. Near the origin, we prove this sequence contracts to a unique fixed point. We explicitly bound the number of iterations required to reach any stopping tolerance, and we quantify the distance from the fixed point to a true Karush-Kuhn-Tucker point, showing this optimality gap vanishes quadratically as the state approaches the origin. Inflating the discrete algebraic Riccati equation generates terminal ingredients that guarantee recursive feasibility and asymptotic stability, even when the solver terminates early. We adapt the terminal penalty online, proving it remains uniformly bounded, and we secure output feedback through the block-observable canonical form, which extracts the exact system state directly from past inputs and outputs. Retaining the block-banded structure of the subproblem forces the computational cost to scale linearly with the horizon length $\ell$. This $O(\ell)$ complexity matches the iterative linear quadratic regulator (iLQR) but sharply undercuts the $O(\ell^3)$ scaling of dense sequential quadratic programming (SQP). Numerical studies on a saturated quadrotor, a nonholonomic integrator, and a nonminimum-phase plant illustrate the theoretical bounds and map how the algorithm compares with iLQR, SQP, and linear-parameter-varying MPC.

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arXiv2023

Output-Feedback Nonlinear Model Predictive Control with Iterative State- and Control-Dependent Coefficients

By optimizing the predicted performance over a receding horizon, model predictive control (MPC) provides the ability to enforce state and control constraints. The present paper considers an extension of MPC for nonlinear systems that can be written in pseudo-linear form with state- and control-dependent coefficients. The main innovation is to apply quadratic programming iteratively over the horizon, where the predicted state trajectory is updated based on the updated control sequence. Output-feedback control is facilitated by using the block-observable canonical form for linear, time-varying dynamics. This control technique is illustrated on various numerical examples, including the Kapitza pendulum with slider-crank actuation, the nonholonomic integrator, the electromagnetically controlled oscillator, and the triple integrator with control-magnitude saturation.

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arXiv2023

Adaptive Output-Feedback Model Predictive Control of Hammerstein Systems with Unknown Linear Dynamics

This paper considers model predictive control of Hammerstein systems, where the linear dynamics are a priori unknown and the input nonlinearity is known. Predictive cost adaptive control (PCAC) is applied to this system using recursive least squares for online, closed-loop system identification with optimization over a receding horizon performed by quadratic programming (QP). In order to account for the input nonlinearity, the input matrix is defined to be control dependent, and the optimization is performed iteratively. This technique is applied to output stabilization of a chain of integrators with unknown dynamics under control saturation and deadzone input nonlinearity.

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arXiv2017

Multivariable Adaptive Harmonic Steady-State Control for Rejection of Sinusoidal Disturbances Acting on an Unknown System

This paper presents an adaptive harmonic steady-state (AHSS) controller, which addresses the problem of rejecting sinusoids with known frequencies that act on a completely unknown multi-input multi-output linear time-invariant system. We analyze the stability and closed-loop performance of AHSS for single-input single-output systems. In this case, we show that AHSS asymptotically rejects disturbances.

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