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Time optimal control based tracking differentiator (TOC-TD) sets a weaker condition on the stability of the systems to be constructed (Han in IEEE Trans Ind Electron 56(3):900–906, 2009, [1], (Guo and Zhao in Active disturbance rejection control for nonlinear systems: an introduction. Wiley, 2016, [2]). Also, it has advantageous smoothness and noise tolerance compared with sliding-mode-based differentiators which may encounter chattering and noise sensitivity problems (Xue et al. in Proceedings of the 29th Chinese control conference. IEEE, pp 6113–6120, 2010, [3]).

Real-time tracking filtering and differentiation estimation of signals are commonly used in the feedback control, the fault detection and isolation and many other fields. In previous work, we have introduced the discrete time optimal control based tracking differentiator in detail.

Real-time differentiation estimation of signals is commonly used in the feedback controller design, the fault detection and isolation and many other control related fields (Han in IEEE Trans Ind Electron 56(3):900–906, 2009, [1]), (Rios et al. in Int J Control 90(2):218–230, 2017, [2]), (Vazquez et al. in IEEE Trans Control Syst Technol 24(5):1740–1750, 2016, [3]). As mentioned in Chap. 2, time optimal control (TOC) based tracking differentiator (TD), first proposed by Jinqing Han, serves not only a transient profile that the system output can reasonably follow to avoid setpoint jump in active disturbance rejection control (ADRC), but also the differentiation acquisition from noise-polluted and/or discontinuous signals.

Time optimal control (TOC) originated from servo control design problems in the 1950s (Hopkin in Trans Am Inst Electr Eng 70(1):631–639, 1951, [1]), (LaSalle in Proc Natl Acad Sci USA 45(4):573, 1959, [2]), and has drawn significant interests in the field of applied mathematics (LaSalle in Contributions to the theory of nonlinear oscillations, vol 5, pp 1–24, 1960, [3]).

The closed-form fhan and Fast algorithms proposed in Chap. 3 were both derived for a discrete-time, double-integral system using the method of isochronic regions; they demonstrate that the solution for DTOC problem is not necessarily a bang-bang control. Also, instead of chattering, the DTOC can produce a smooth control signal that results in the performance similar to that of the bang-bang control.

Today’s transportation section accounts for a significant portion of petroleum consumption and greenhouse gases emissions worldwide. Statistics show that \(63.7\%\) of the petroleum consumed in the world in 2012 was due to the transport sector, which caused emission of 7135 million tons of carbon dioxide into the environment (International energy agency: key world energy statistics (2014), [1]). The world’s fossil fuel scarcity, as well as the growing environmental crisis associated with their wide usage, is driving the electrification of transportation and extensive use of electric vehicles (EVs). EVs are emerging as an efficient and sustainable alternative for private and public road transportation.

Microgrids are expected to be more robust and cost-effective than the traditional approach of centralized grids. However, a number of technical and regulatory issues have to be resolved before the microgrid can become a commonplace.

Energy generation scheduling to achieve robust and economic power supply is an essential component in microgrids. Two features of microgrids are the integration of large-scale renewable sources and the use of combined heat and power (CHP) generators. Such features, however, impose significant difficulties on the design of intelligent control strategies for microgrids.

In this chapter, we summarize this book and discuss the future work for intelligent control of microgrids and scheduling of EVs’ charging.

In the world today, fossil fuels are the dominant energy sources for both transportation sector and electricity generation industry.