Nonlinear Integral-Ameliorated Model for Dynamic Convex Optimization With Perturbance Considered

This work presents a nonlinear integral-ameliorated model for handling dynamic optimization problems with affine constraints. They pose a challenge as their optimal solutions evolve with time. Traditional iteration-based methods that exactly solve the problem at each time instant, fail to precisely and real-time track the solution due to computational and communication bottlenecks. Our model, through rigorous theoretical analyses, is able to reduce the optimality gap (i.e., the difference between the model state and optimal solution) to zero in a finite time, and thus, track the solution online. Besides, perturbance is taken into account. We prove that under certain conditions, our model can totally tolerate an important kind of noise that we call “error-related noise”. In numerical experiments, compared with six existing methods, our model exhibits superior robustness when contaminated by the error-related noise. The key techniques in the model design involve employing the zeroing neural network to leverage time-derivative information, and introducing an integral term as well as the class $ {{{\mathrm{C}}}^0_\text{L}} $ functions to enhance convergence and noise resistance. Finally, we establish a model-free control framework for a surgical manipulator with the remote-center-of-motion constraint and compare the performances of the framework based on different models in simulations. The results indicate that our model achieves the best performance among various models employed within the framework.