# A Survey: Future Smart Cities Based on Advance Control of Unmanned Aerial Vehicles (UAVs)
## 5 Why Nonlinear Control Strategies
### History of Nonlinear Control  
The centrifugal \"flyball\" governor, which was created in the 18 th century to manage steam engines by regulating the steam admittance to the cylinder, is the precursor to nonlinear control. But at that time, the governor did not use any particular analytic ideas [36]. Russian mathematician [PERSON] developed two techniques in 1892 for assessing the stability of dynamic systems given by ordinary differential equations (ODE). The second approach, often known as the [PERSON] direct method, enables stability analysis of nonlinear control systems without the requirement to solve the ODE directly, opening up a wide range of potential applications [87]. According to [PERSON], the genuine nonlinear system will likewise be stable in a specific area around an equilibrium point if the linear approximation of the system is stable there. His writings were translated into French in 1907, and [PERSON] and [PERSON] later rediscovered them in relation to control. [PERSON]'s study of electronic oscillations and [PERSON]'s findings on nonlinear vibration both made significant contributions to nonlinear control. Several methods were created to comprehend and forecast diverse phenomena displayed by nonlinear systems, building on the presented nonlinear second-order equations. Subharmonic oscillations, limit cycles, jump phenomena, and frequency entrainment are a few examples of these phenomena. The scientific community did not start tackling the problem of controlling servomechanisms until the late 1930s, when the field of control engineering was still in its infancy [88]. The phase plane method developed by [PERSON] was used to analyse these mechanisms, which were roughly represented by second-order systems. Research on nonlinear control of servomechanisms advanced significantly with the outbreak of World War II. Intensified investigations were spurred by the functional requirements put forth by fire-control systems and the operation of guided vehicles. The description function, the phase plane method, and other methods utilizing relay systems were the three main analytical techniques used between 1940 and 1960 for the analysis of nonlinear systems. In the classical era, linear, finite-dimensional, time-invariant systems with single inputs and outputs were used to solve the majority of issues. The year 1960 marked the beginning of the modern era for nonlinear control [78]. Additionally, the inaugural IFAC (International Federation of Automatic Control) convention was taking place in Moscow at the same time. This invention helped modern control theory to emerge by bringing the theories of physics and Nyquist-Bode feedback closer together. Applications in this era were primarily driven by the space race and the defense industry. Numerous industrial sectors, including those producing cars, ships, steel, paper, and minerals, also used nonlinear control. Due to their nonlinear, time-varying, high-dimensional, poorly modeled, and multivariable nature, the encountered real systems presented difficulties and were outside the scope of classical control theory. The development of digital computers began as a design tool and eventually evolved into a crucial part of control systems. Scientists used the Lyapunov theory in the early 1970s to investigate how the ideas of energy and dissipation relate to one another. They found that dynamic systems might be seen as energy transformational mechanisms. [PERSON] developed a hypothesis for dissipative systems based on this concept [78]. [PERSON] and [PERSON] developed the notion of input-to-state stability for nonlinear control systems throughout the 1990s [82]. This theory makes it possible to analyze the stability of complex structures using the actions of simple subsystems. Applications in biological and chemical processes have been successful [89]. [PERSON] introduced the idea of zero dynamics to geometric control theory in 1995 [83].