About

Tong Ma is an Assistant Professor in the Department of Mechanical and Industrial Engineering at Northeastern University College of Engineering, having joined the faculty in July 2022. His research focuses on dynamics, control, and artificial intelligence for automation, with particular emphasis on networks and complex systems, robotics, and controls systems. He holds a PhD in Mechanical Engineering from the University of Connecticut, earned in 2018. His work involves the development of adaptive neural fault-tolerant control methods for uncertain multivariable nonlinear systems, as well as filtering adaptive tracking controllers for multivariable nonlinear systems subject to constraints and uncertainties. His contributions include advancing the understanding and application of control theories and AI techniques to improve automation systems' robustness and performance.

Research topics

• Artificial Intelligence
• Computer Science
• Mathematics
• Machine Learning
• Meteorology
• Engineering
• Applied mathematics
• Physics
• Control engineering
• Mathematical optimization
• Algorithm
• Statistics

Selected publications

• Stochastic load frequency control of power systems via Gaussian processes

  International Journal of Control · 2025-10-07

  article1st authorCorresponding
  PublisherDOI

• Closed-form adaptive tracking control of heat equations aided by Fourier regularization and bi-orthogonal series

  Automatica · 2025-04-23

  article1st authorCorresponding
  PublisherDOI

• Closed-Form Adaptive Tracking Control of Heat Equations Aided by Fourier Regularization and Bi-orthogonal Series*

  2025-07-08

  article1st authorCorresponding

  This paper proposes a closed-form adaptive tracking control approach for linear heat equations with unknown parameters to achieve full temperature profile tracking by leveraging Fourier regularization and bi-orthogonal series. A state predictor which copies the plant with unknown parameters replaced by their estimates is built and an adaptive law is designed to estimate the unknown parameters. The state predictor is decomposed into two subsystems for tracking control synthesis: the first subsystem involves terms from the original heat equation, while the second subsystem is simpler and can be reformulated as a standard heat equation. Specifically, the first subsystem is regarded as an unforced partial differential equation whose terminal states always follow the desired temperature profile such that its initial condition can be calculated by solving the backward heat equation at every time step. To address the blow-up issue in backward calculation, a Fourier regularization scheme is explored to cut off the higher-order Fourier modes and an appropriate tradeoff between approximation accuracy and robustness is achieved. Given the solutions from the first subsystem, the initial condition for the second subsystem can be subsequently calculated. We propose a numerical algorithm to calculate a set of bi-orthogonal series offline and employ them to compute the boundary control function that drives the second subsystem to zero at every time step. Combining these two subsystems, it guarantees that the overall system follows the desired temperature profile. We demonstrate that the proposed closed-form adaptive tracking control algorithm achieves full temperature profile tracking with < 2% error.

  PublisherDOI

• Constrained Load Frequency Control in Power Systems via Integrated Stochastic Model Predictive Control and Unscented Kalman Filter

  2025-07-08

  articleSenior author

  By incorporating the unscented Kalman filter (UKF) into the stochastic model predictive control (SMPC) architecture, a UKF-SMPC framework is formulated to solve the load frequency control (LFC) problem of a power system subject to wind resources and load disturbances. To suppress the frequency deviations resulting from the stochastic uncertainties and reduce the mechanical power cost, a finite-horizon constrained optimization problem is formulated to maintain the stability of the power system and improve the overall performance. Considering the stochastic nature of wind resources and load disturbances, the UKF is incorporated into the SMPC directly to estimate the states and to propagate the mean and covariance of the states forward in time by taking the state estimation errors and additive noise from the disturbances into consideration. The statistical description including the mean and covariance estimates of the state provided by the UKF are employed to reformulate the cost function and chance constraints. By resorting to the Chebyshev-Cantelli inequality, the chance constraints on the load frequency deviation are reformulated as deterministic ones, which are subsequently linearized at the cost of additional conservativeness. To guarantee the convergence and recursive feasibility of the UKF-SMPC framework, two kinds of terminal constraints are applied, that is, "robust horizon" and Lyapunov equation. By resorting to the Schur complement, the finite-horizon constrained optimization problem is recast as a linear one with a set of linear matrix inequalities (LMIs), which yields a Semidefinite Programming (SDP) problem. Simulation results validate the effectiveness of our approach.

  PublisherDOI

• Chance constrained load frequency control of power systems with wind resources

  Journal of the Franklin Institute · 2024-12-24 · 3 citations

  article1st authorCorresponding
  PublisherDOI

• Computationally Tractable Gaussian Process-based Stochastic Predictive Control Using Backoffs

  IFAC-PapersOnLine · 2024-01-01

  articleOpen accessSenior authorCorresponding

  Current stochastic nonlinear model predictive control (SNMPC) hinges on the lack of high-fidelity models that describe the system behavior and the lack of tractable solution methods that handle chance constraints. Motivated by this, a model-and data-driven predictive control approach using Gaussian processes (GP-MDPC) is synthesized in this paper. It exploits GPs to learn the unknown dynamics and apply Taylor expansion for uncertainty propagation through probabilistic modeling. A backoff approximation method is explored to reformulate the chance constraints into tractable expressions. Finally, a finite-horizon stochastic optimal control problem (FH-SOCP) is formulated.

  PublisherDOI

• Optimization of PID Parameter Tuning Based on Improved Dung Beetle Algorithm

  2024-07-26 · 2 citations

  article1st authorCorresponding

  The Dung Beetle Optimizer (DBO) algorithm is a powerful metaheuristic. Although DBO offers quick convergence and excellent optimization capabilities, excessive overshoot and significant disturbance in the PID parameter adjustment have two drawbacks. To address the issue of PID parameter optimization, this study introduces an enhanced DBO technique known as the Improved Chebyshev Dung Beetle Optimizer (ICDBO). This study used the golden sine strategy to improve the global search capability of rolling behavior, increase the search range, and decrease the likelihood of adding perturbations. It also uses an improved Chebyshev chaotic mapping initialization population and a dynamic weighting strategy to ensure the flexibility of the algorithm. The algorithm was tested using three benchmark test functions to confirm ICDBO’s efficacy. These results demonstrated the strong functionality of the ICDBO algorithm. Finally, the ICDBO method was successfully applied to PID parameter-tuning optimization to further explain the practical application potential of the technique. The experimental findings demonstrate that compared to the conventional DBO method, the proposed ICDBO algorithm enhances system stability and minimizes overshoot.

  PublisherDOI

• High-gain Output Feedback Control Design for a Class of Uncertain Nonlinear Systems Using Gaussian Processes *

  2023-05-31

  article1st authorCorresponding

  This paper considers the tracking control problem of a class of uncertain nonlinear systems with partial noisy measurements. To cope with the uncertainties including the unknown nonlinear dynamics and unmeasured state variables, simultaneous estimation of all the hidden states and unknown dynamics are required for the controller design. In this paper, a high-gain observer delivers a good property of disturbance rejection and provides state estimates which serves as the training data for learning the unknown dynamics. Because the measurements are corrupted by noise, this leads to estimation error in the state estimates. Since the Gaussian process (GP) has high flexibility to capture the complex unknown functions by using very few parameters and it inherently handles measurement noise, GP model is employed to learn the unknown dynamics from the state estimates. This provides critical information for the control design such that the unknown dynamics is compensated and a good tracking performance is delivered. In short, the high-gain observer provides state estimates for the GP model to learn the unknown dynamics from noisy measurements, which enables the development of the controller. Comparisons against ℒ<inf>1</inf> adaptive control and high-gain output feedback controller without GP learning are carried out.

  PublisherDOI

• Tracking control of uncertain nonlinear systems via adaptive Gaussian process prediction and real-time optimisation

  International Journal of Control · 2023-12-18 · 1 citations

  article1st authorCorresponding

  Control of nonlinear systems in the presence of model mismatch and system constraints is quite challenging. To address the issue, this work proposes an adaptive Gaussian process-based real-time optimisation (AGP-RTO) control framework. Specifically, the control law consists of two components, a feedforward tracking control law and an uncertainty compensation control law. Because GP has high flexibility to capture complex unknown functions by using very few parameters and it inherently handles measurement noise, this work utilises the GP as an alternative to estimate the mismatch between the real plant and the approximated model. During every RTO execution, the GPs adaptively update the predictions of the model mismatch, then the predictions are embedded into a nonlinear optimisation problem for the correction of the model cost and constraint functions, which yields the uncertainty compensation control law. The proposed AGP-RTO framework ensures that the Karush-Kuhn-Tucker (KKT) conditions determined by the model match those of the plant upon convergence. Compared to many direct adaptive control methods, AGP-RTO does not rely on a high gain for fast adaptation and hence it improves the robustness of the closed-loop system. Compared to the modifier adaptation (MA) method, AGP-RTO avoids the plant-gradient estimation by using the finite difference scheme, besides it trains the GP models offline, which speeds up online evaluation and improves the applicability and efficacy of real-time control. Comparisons are carried out to illustrate the superiority of the AGP-RTO.

  PublisherDOI

• A model‐and data‐driven predictive control approach for tracking of stochastic nonlinear systems using Gaussian processes

  International Journal of Robust and Nonlinear Control · 2023-06-22 · 7 citations

  article1st authorCorresponding

  Abstract Nonlinear model predictive control (NMPC) is one of the few control methods that can handle complex nonlinear systems with multi‐objectives and various constraints. However, the performance of NMPC highly depends on the model accuracy and the deterministic solutions may suffer from conservatism, for example, robust MPC only considers the worst‐case scenario, which yields the NMPC not working efficiently in uncertain stochastic cases. To address these issues, a model‐and data‐driven predictive control approach using Gaussian processes (GP‐MDPC) is synthesized in this paper, which copes with the tracking control problems of stochastic nonlinear systems subject to model uncertainties and chance constraints. Because GP has high flexibility to capture complex unknown functions and it inherently handles measurement noise, GP models are employed to approximate the unknowns, the predictions and uncertainty quantification provided by the GPs are then exploited to propagate the uncertainties through the nonlinear model and to formulate a finite‐horizon stochastic optimal control problem (FH‐SOCP). Specifically, given the GP models, closed‐loop simulations are executed offline to generate Monte Carlo samples, from which the back‐offs for constraint tightening are calculated iteratively. The tightened constraints then guarantee the satisfaction of chance constraints online. A tractable GP‐MDPC framework using back‐offs for handling nonlinear chance constrained tracking control problems is yielded, whose advantages include fast online evaluation, consideration of closed‐loop behaviour, and achievable trade‐off between conservatism and constraint violation. Comparisons are carried out to verify the effectiveness and superiority of the proposed GP‐MDPC scheme with back‐offs.

  PublisherDOI

Frequent coauthors

• Chengyu Cao

  University of Connecticut

  13 shared

• Alexandre M. Tartakovsky

  8 shared

• David A. Barajas‐Solano

  7 shared

• Yuqian Liu

  Xiangya Hospital Central South University

  6 shared

• Xingwei Wang

  6 shared

• Jingcheng Zhou

  5 shared

• J. Nathan Kutz

  3 shared

• Daniel Dylewsky

  University of Waterloo

  3 shared