# Synergetic Synthesis of Nonlinear Laws of Throttle Control of a Pneumatic Drive
## 1 Introduction
### Fuzzy Adaptive Control  
In recent decades, the development of microprocessor technology has led to improvement of regulator tuning algorithms. Now, there are industrial controllers with automatic tuning of the parameters of mobile robotic systems using adaptive algorithms, neural networks, fuzzy logic methods, and genetic algorithms [12; 13; 14; 15].  
In [16], a path-tracking controller with geometric constraints and built-in intelligence for collision avoidance was proposed based on a dual hybrid control law. The hybrid control law combines a linearization feedback controller with a fuzzy logic controller. The feedback linearization controller helps the mobile robot stay on the target path, and the fuzzy logic controller helps the mobile robot avoid critical obstacles on the reference path.  
Due to intractable errors in approximating nonlinear dependencies, existing controllers may receive only limited results and require speed feedback to perform an online estimate. To overcome the drawbacks, in [17], a new controller with output feedback was developed to accurately track the trajectory and obtain state estimates for the class of Euler-Lagrange mechatronic systems. Firstly, a group of auxiliary variables was created to reconstruct velocities without numerical differential operations accurately. Then, unknown model information and dead zones/drive faults are simultaneously approximated online using only the available output information.  
The authors of [18] propose a fuzzy control method for undefined nonlinearity, unknown modeling parameters, and an inaccessible state. First, an interval fuzzy logic system type 2 (IT2 FLS) and a state observer based on the IT2 FLS are created to estimate the systems' uncertain nonlinearity and unavailable state. A target performance control (PPC) method is then proposed to achieve the target tracking characteristics of steer-by-wire (SbW) systems.  
A hypersonic apparatus is considered in [19] as a typical nonlinear and indefinite model, which has parameters and characteristics of strong coupling that change rapidly over time. The authors proposed an adaptive method for compensating unknown disturbances of the aircraft model in real time and improving control characteristics by developing a nonlinear control law. The tracking differentiator smoothly tracks the manipulated variable error, and an extended state observer is created based on the unknown disturbances to perform a single real-time estimate. The nonlinear controller improves control efficiency and allows the controlled object to quickly and stably track the trajectory. Simulation results for a hypersonic vehicle controller demonstrate that fuzzy ADRC (FADRC) has an advantage in tracking speed and effect over traditional methods and simplifies the ADRC parameter design process.  
Active noise cancellation control (ANCC) is used in attitude control of a quadcopter to solve the problem of destabilization in flight control [20]. The authors proposed an algorithm for fractional optimization of a swarm of fuzzy particles to optimize ANCC parameters for quadcopters. In addition, a turbulent airflow model has been created to test the effectiveness of the suppression of disturbances by the controller. After optimizing the parameters with the proposed algorithm, the results show that the regulator has a small overshoot and a stronger interference suppression ability.  
The disadvantages of controllers based on fuzzy logic include: the impossibility of mathematical analysis of fuzzy systems using existing methods, a slight increase in accuracy compared to the probabilistic approach, and increasing the number of input variables increases the computational complexity exponentially, making it difficult to comprehend.