Ankit Goel

Turibius Rozario, Arjun Trivedi, Ankit Goel

This paper presents a compact, matrix-based representation of neural networks in a self-contained tutorial fashion. Specifically, we develop neural networks as a composition of several vector-valued functions. Although neural networks are well-understood pictorially in terms of interconnected neurons, neural networks are mathematical nonlinear functions constructed by composing several vector-valued functions. Using basic results from linear algebra, we represent a neural network as an alternating sequence of linear maps and scalar nonlinear functions, also known as activation functions. The training of neural networks requires the minimization of a cost function, which in turn requires the computation of a gradient. Using basic multivariable calculus results, the cost gradient is also shown to be a function composed of a sequence of linear maps and nonlinear functions. In addition to the analytical gradient computation, we consider two gradient-free training methods and compare the three training methods in terms of convergence rate and prediction accuracy.

Parham Oveissi, Turibius Rozario, Ankit Goel

The application of neural networks in modeling dynamic systems has become prominent due to their ability to estimate complex nonlinear functions. Despite their effectiveness, neural networks face challenges in long-term predictions, where the prediction error diverges over time, thus degrading their accuracy. This paper presents a neural filter to enhance the accuracy of long-term state predictions of neural network-based models of dynamic systems. Motivated by the extended Kalman filter, the neural filter combines the neural network state predictions with the measurements from the physical system to improve the estimated state's accuracy. The neural filter's improvements in prediction accuracy are demonstrated through applications to four nonlinear dynamical systems. Numerical experiments show that the neural filter significantly improves prediction accuracy and bounds the state estimate covariance, outperforming the neural network predictions. Furthermore, it is also shown that the accuracy of a poorly trained neural network model can be improved to the same level as that of an adequately trained neural network model, potentially decreasing the training cost and required data to train a neural network.

Alexander Dorsey, Ankit Goel

This paper develops a guidance law for nonlinear interception using input-output feedback linearization (IOL). The engagement between a pursuer and an evader is modeled using point-mass dynamics, and a baseline IOL-based guidance law is constructed by regulating the angular rates of the line-of-sight (LOS) vector. While this approach yields stable input-output behavior, it does not constrain the internal (zero) dynamics of the system, which can result in non-intercepting trajectories despite successful regulation of the LOS rates. To address this limitation, a modified IOL-based guidance law is proposed that incorporates a correction mechanism to enforce convergence of the range. The resulting formulation ensures that LOS alignment corresponds to a closing trajectory, thereby enabling convergence of the pursuer to the evader for a broad class of initial engagement geometries. The proposed method retains the computational simplicity and real-time implementability of feedback linearization while improving closed-loop performance relative to classical guidance laws. Extensive Monte Carlo simulations over a wide range of initial conditions are conducted to evaluate the proposed method. The results demonstrate improved reliability, reduced miss distance, and consistent convergence compared to the baseline IOL and classical proportional navigation.

Parham Oveissi, Ankit Goel

This paper presents a model-free, data-driven control synthesis method called dynamic mode adaptive control (DMAC) for systems whose mathematical models are unavailable or unsuitable for classical control design. The proposed approach combines data-driven dynamics approximation with adaptive control synthesis to enable online controller design using measured system data. DMAC comprises two main components: a dynamics-approximation module and a controller-synthesis module. The dynamics approximation module estimates a local linear representation of the system dynamics directly from measurements using a matrix recursive least-squares algorithm with a forgetting factor. The estimated dynamics are then used to compute an online stabilizing controller with full-state feedback and integral action. Theoretical analysis establishes convergence properties of the recursive dynamics approximation and boundedness of the closed-loop system under the DMAC controller. The performance of the proposed method is demonstrated through numerical examples involving representative dynamical systems, including an unstable linear system, the Van der Pol oscillator, and the Burgers' equation. Sensitivity studies further demonstrate the robustness of DMAC with respect to both algorithm hyperparameters and variations in system parameters.

August Phelps, Juan Augusto Paredes Salazar, Ankit Goel

Optimal trajectories that minimize a user-defined cost function in dynamic systems require the solution of a two-point boundary value problem. The optimization process yields an optimal control sequence that depends on the initial conditions and system parameters. However, the optimal sequence may result in undesirable behavior if the system's initial conditions and parameters are erroneous. This work presents a data-driven fuzzy controller synthesis framework that is guided by a time-optimal trajectory for multicopter tracking problems. In particular, we consider an aggressive maneuver consisting of a mid-air flip and generate a time-optimal trajectory by numerically solving the two-point boundary value problem. A fuzzy controller consisting of a stabilizing controller near hover conditions and an autoregressive moving average (ARMA) controller, trained to mimic the time-optimal aggressive trajectory, is constructed using the Takagi-Sugeno fuzzy framework.

Joonghyun Lee, John Spencer, Juan Augusto Paredes et al.

This paper develops an adaptive digital autopilot for a fixed-wing aircraft and compares its performance with a fixed-gain autopilot. The adaptive digital autopilot is constructed by augmenting the autopilot architecture implemented in PX4 flight stack with adaptive digital control laws that are updated using the retrospective cost adaptive control algorithm. In order to investigate the performance of the adaptive digital autopilot, the default gains of the fixed-gain autopilot are scaled down to degrade its performance. This scenario provides a venue for determining the ability of the adaptive digital autopilot to compensate for the detuned fixed-gain autopilot. Next, the performance of the adaptive autopilot is examined under failure conditions by simulating a scenario where one of the control surfaces is assumed to be stuck at an unknown angular position. The adaptive digital autopilot is tested in simulation, and the resulting performance improvements are examined.

John Spencer, Joonghyun Lee, Juan Augusto Paredes et al.

This paper develops an adaptive PID autotuner for multicopters, and presents simulation and experimental results. The autotuner consists of adaptive digital control laws based on retrospective cost adaptive control implemented in the PX4 flight stack. A learning trajectory is used to optimize the autopilot during a single flight. The autotuned autopilot is then compared with the default PX4 autopilot by flying a test trajectory constructed using the second-order Hilbert curve. In order to investigate the sensitivity of the autotuner to the quadcopter dynamics, the mass of the quadcopter is varied, and the performance of the autotuned and default autopilot is compared. It is observed that the autotuned autopilot outperforms the default autopilot.

Ankit Goel, Abdulazeez Mohammed Salim, Ahmad Ansari et al.

This paper develops an adaptive autopilot for quadcopters with unknown dynamics. To do this, the PX4 autopilot architecture is modified so that the feedback and feedforward controllers are replaced by adaptive control laws based on retrospective cost adaptive control (RCAC). The present paper provides a numerical investigation of the performance of the adaptive autopilot on a quadcopter with unknown dynamics. In order to reflect the absence of prior modeling information, all of the adaptive digital controllers are initialized at zero gains. In addition, moment-of-inertia of the quadcopter is varied to test the robustness of the adaptive autopilot. In all test cases, the vehicle is commanded to follow a given trajectory, and the resulting performance is examined.