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Description
Differential Games: A Concise IntroductionThis book uses a small volume to present the most basic results for deterministic two person differential games. The presentation begins with optimization of a single function, followed by a basic theory for two person games. For dynamic situations, the author first recalls control theory which is treated as single person differential games. Then a systematic theory of two person differential games is concisely presented, including evasion and pursuit
This book uses a small volume to present the most basic results for deterministic two-person differential games. The presentation begins with optimization of a single function, followed by a basic theory for two-person games. For dynamic situations, the author first recalls control theory which is treated as single-person differential games. Then a systematic theory of two-person differential games is concisely presented, including evasion and pursuit problems, zero-sum problems and LQ differential games.
The book is intended to be self-contained, assuming that the readers have basic knowledge of calculus, linear algebra, and elementary ordinary differential equations. The readership of the book could be junior/senior undergraduate and graduate students with majors related to applied mathematics, who are interested in differential games. Researchers in some other related areas, such as engineering, social science, etc. will also find the book useful.
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4.5 ★★★★★
Based on 20 reviews
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Product Reviews
★★★★★ 4
Impressive Cleaning, but not quite perfect
UPDATE BELOW INITIAL REVIEW
This is an impression after having run 6 sessions total over the span of two days on a 3 story home, two days after product release.
I want to get something out of the way first: I have never owned a robovac; I have friends that have and I have witnessed them in action, but not my own. I recently moved into a big home with my SO and we quickly realized we would need some serious cleaning assistance. I set off in search of a good robovac, scouring the internet for hours over a week. Everything pointed to this vacuum.
I read some pretty unbelievable reviews, and let me tell you they're not entirely accurate from my experience, but pretty darn close.
Upon setting up my S7 MaxV I was immediately greeted with a firmware update, which went without a hitch and provided a changelog. Good sign, as this means that we should be able to expect OTA improvement over time. I have very long hair, we have no pets, but we leave a lot of things around the house and there are a lot of potential things to hit and get stuck on such as standing fans, chairs, tables, electronics, metal floor vents, etc for the vac to interact with on every floor. Everything this vacuum promises lives up to expectations, but there are a few caveats. It will get hung up on some things, still, such as metal floor heater grates and long Ethernet (any really) cables stretched across the floor, and it is definitely not immune to the amazing power of long hair and it's evil tangling powers. That said, it is surprising easy to remove long hair from both the side and middle brushes, albeit I did have to carefully cut the hair on the middle brush to get most of it off.
As to cleaning, it's incredible on all surfaces. You can really hear the power of the vacuum roar to life on carpet, where it auto switches to higher suction when moving off another surface. Not much to say here other than things were spotless after it mopped and vacuumed about 66sq meters in 1hr, including underneath large objects. Way better than me!
Obstacle avoidance is almost flawless, I didn't really need to monitor this at all. Additionally, it detected stairs very well.
The video camera and call functions are pretty neat, but don't expect too much out of them as it's mostly a gimmick. Fun though!
There's just so much to say but I will cut to the chase: this robovac is freaking incredible. I am extremely satisfied with my purchase, and am excited for the ultra dock that supposedly comes out next month. If you are on the fence, this robovac is well worth it! That said, it is extremely expensive but if you can shell it out you will likely be satisfied, too!
---UPDATE AS OF May 12 2022:
The robovac is working as great as ever for it's main purpose--cleaning. Maintenance has been am absolute breeze; after three to six runs you empty the dustbin and after every mop you clean it. As mentioned above, I have long hair so I occasionally need to take out the main and side brushes, but cleaning these takes about 2 minutes. Refilling the water tank with distilled water takes about 10 seconds. I've noticed that a few features don't work properly, even with perfect signal (wifi or cell), such as the calling and remote viewing features. It's simply will not display the video no matter what I do. At one point I was able to get it to work by cycling my Wi-Fi and cellular a bunch of times and eventually it showed. I have not tested this on iOS, but at least on Android it does not work properly. Additionally the vacuum has managed to lose its main brush on a metal floor transition strip. My theory is that it got caught on the nails holding the strip. Honestly this was a pretty minor inconvenience. I still think this robot vacuum deserves four stars, however there are a few things I would really like to have:
1. An undo button on the map, as well as an option to manually erase parts of mapped areas (think like the eraser tool in your favorite image editor). As someone that has quite a few full sliding door mirrors, the robot vacuum loves to see "into them" and see those "inside mirror parts as part of the room. This has led it to bleed into other rooms which has led me to have to remap. Minor inconvenience as it's fixable by putting down things to block the robots view of the mirror but rather annoying.
2. An option to disable the mop without removing it. While I generally like it to mop, sometimes I just don't need it for what I needed to do.
Overall great product, would buy more from Roborock.
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Reviewed in the United States on April 11, 2022
★★★★★ 5
Excellent Choice In A Reasonably Priced Robot Floor Cleaner
Color: Black01, Color: Black01
This review is for the Roborock QV3a. After hearing my brother-in-law rave about his robot vacuum, I hesitantly bought this. I was hesitant because I had purchased one many years before, and it had been virtually useless. It only vacuumed, was loud with minimal suction, banging its way around and it constantly got clogged with debris and eventually ended up at Goodwill. This vacuum does a wonderful job both vacuuming and mopping, competing with models that cost three times as much. After creating four different maps, the first map, map with the 1st floor family room, kitchen and dining room room all on one level, I segregated an area of the kitchen that gets very dirty after cooking, to allow me to do a daily vacuuming and mopping of this area. The second map included a living room off of our raised entry hall. The third map included the raised tiled entry hall. The fourth map included the second level of the house, including three bedrooms and a large balcony.We have biweekly housekeeping, so most of yhe areas of the house, including a carpeted living room, tile entry hall, living room, 4 bedrooms and balcony, only require vacuuming as needed, often once in the week we don’t have housekeeping. After completing a cleaning of the whole house I was very impressed. It thoroughly cleaned including under furniture picking up an amazing amount of dust bunnies. Our regular vacuum did not fit under dressers, couch, couches, etc. Mopping the tile areas resulted in very clean floors. I did established some no go areas to keep the vacuum from hitting areas with a large number of cords. I also created no go areas under the beds and a couple dressers. Avoiding these areas, greatly speeds up the cleaning process. It is easy to establish no go areas. I can delete them a couple times a year to clean under furniture. I also put up an invisible line on the railing in our balcony, the robot did not see this as a wall, and it would feel its way along the railing, greatly slowing the cleaning process. The robot does seems to learn each time it cleans finding a more efficient way to clean. I also found that moving the chairs away from the dining room table slightly allowed the robot to clean under the table much faster. Our family room has a very large area rug in it with hardwood floors throughout. The robot was able to identify the rug area, mopping/vacuuming hardwood floors and vacuuming the area rug. The app is very intuitive easily allowing the establishment of no goes zones or invisible walls. To clean, simply restore the map for the area you want to clean, select the area you want to clean, and choose your cleaning mode of mopping, vacuuming, or both. It is very simple to use. When done the robot empties the dirty water, cleans the mopping pads, and empties the dust bin. I am very happy with my purchase. For anyone that wants to purchase a cleaning robot without spending $1000 or more, this is an excellent choice. Update: after over 30 hours of use I am still pleased with this robotic floor cleaner. Use daily to keep kitchen tile floor vacuumed. Mop cycle cleans tiles as well as a mop using highest water setting. Also great for cleaning hardwood floor and carpet. Great value for the price. No problems to report. Buy one!
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Reviewed in the United States on January 24, 2026
★★★★★ 5
Absolute Yes for Me
Color: Black
The kids have named our vacuum ROB. And ROB is a total Workhorse. Extremely simple setup, in my opinion. Caveat: it does not work or sync with 5g signal, but it will still work generally. In other words, it will still work the same, but will not remember floor layouts. So each time you turn it on, it is not following a learned “map”. If you’re okay with it not following that map each time, then this vacuum will take great care of your floors. In my opinion, this does not affect the functionality. The Lefant Vac is impressive. It doesn’t stop at hard flooring, either— it crosses over transition strips to low- medium pile carpet and does a great job keeping the carpet clean as well. The battery life is also impressive— going for a couple hours before returning to the charging station. I can still program it to clean at certain times, but I don’t use that option. The suction power is excellent, and it has picked up long hair fur from my ex’s German Shepherd that my upright vacuum didn’t catch. Noise level is fine. I’m not losing my mind over it at all. In fact, after a few minutes of it running, I’ve forgotten all about it until it returns to the dock. ROB is able to maneuver very well around furniture and doorways. Just make sure you don’t leave anything on the floor that you don’t want sucked up. Because it will get EVERYTHING in its way. I purchased this vacuum on sale back in November 2025 and I’m so glad I took a chance on it. Best thing I’ve ordered in a while and the price couldn’t be beat. Far superior to my old Roomba. I haven’t used the wet mop setting yet since I haven’t needed it— couldn’t tell you how well that works. The dirt canister is pretty easy to empty, but bring the whole vacuum to the garbage can to empty since it can get kind of messy the first couple times you empty it, especially depending on how much dirt it’s picked up. I bought this robot vacuum for my vinyl kitchen flooring, but once I realized it was able to do far more and had conquered my medium pile carpet just as easily, the is vacuum regularly cleans my entire downstairs flooring in one charge. Jump on this if you can. I highly recommend this vacuum
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Reviewed in the United States on March 15, 2026
★★★★★ 5
A very good product, which fulfills its purpose and even more so if bought on sale.
Color: Black
I bought the vacuum cleaner from abroad, without really knowing it or having seen it, only from the reviews I read on Amazon. The product arrived perfectly packaged, on time and in perfect condition.
The manual is simple and has clear instructions, correctly translated from Chinese to English, so it wasn't difficult to get it up and running. It came with everything the box stated: charger, cable, mop liquid container, floor mop, two sets of brushes, and a HEPA filter. This same filter has a very thin foam filter, which unfortunately broke the third time I cleaned it with a brush: this seems to be normal, and the brand should review its specifications.
It's essential to place the base in a location where the device can be easily returned and where there aren't too many clutter around it to avoid problems. Install Lefant's proprietary app, and following the step-by-step instructions makes it easy to connect to Wi-Fi and your cell phone. This allows you not only to give commands to the robot but also to schedule different cleanings, check the map the vacuum cleaner is creating, etc.
Regarding the location system, the LIDAR is really good at generating a real-time map as it scans the terrain the first time we turn it on; that's why it's essential to choose the right resting and charging location, otherwise we'll have to redo the map if we move it. As the vacuum cleaner moves, it generates this map that automatically detects the rooms, although it also has an editing system that allows it to do this, determining the cleaning order for each room, blocking off areas, etc. The map is updated with each pass the robot makes, and the phone's software is responsible for correctly "determining" some lines on it, as well as independent spaces. One detail: in my case, the vacuum cleaner thinks the space under the main bed is another room, so I can ask it to clean the entire room or just that space.
Cleaning is effective, with two effective brushes and adequate suction power for daily, non-deep cleaning. It has three power levels: a quiet one, a normal one, and a powerful one. Generally speaking, normal vacuuming is enough for an average home with the usual crumbs, dust, and pet hair. In this regard, I have a long-haired cat, and it's noticeable how time and again when the robot vacuums, I find tons of loose hair and dirt: this situation has really improved in my home. The battery life is adequate, although in a 50 square meter area, I've seen that when using the highest suction power, when it reaches 60% of the remaining battery, it decides to recharge (I don't know why or if it's a programming glitch).
If you have long-pile carpets, it's advisable to lift them off the floor and not let the vacuum cleaner pass near or over them, as the brushes get tangled in the long hair, causing it to jam and prevent it from cleaning further. Although it has a carpet mode, it's designed for hard and short-pile carpets, where it basically increases the suction power. But, again, this is a problem with long-pile carpets. Regarding this, when the vacuum cleaner gets stuck or detects a situation it can't resolve, it emits a voice alert clarifying the situation, and a notification is sent to the phone, more specifically to the dedicated app. This app is very comprehensive and allows you to view real-time and aggregated statistics on the robot's work. I must say that the Chinese to English translation is better than the Spanish one, so I recommend using it in English.
I haven't used the mop enough to comment, but from the little I've used it, it's accurate in terms of the amount of liquid and the way it's distributed. You can add some kind of cleaner, as long as it's light, not sticky, and doesn't leave residue.
In conclusion, it's a purchase I recommend, a good product that fulfills its purpose. If I could improve it, I would make it come with a larger number of spare parts or make them easier to purchase, since it doesn't have much information and when looking for them, you have to rely on other brands or models.
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Reviewed in the United States on September 16, 2025
★★★★★ 4
Keeps clean with 5 cats
Color: Black, Color: Black
I like this vacuum - a very convenient solution to the issue of 5 cats leaving their hairs all over my house. The mop feature is mostly useless though, so I can’t give it a full 5 stars.
Pros:
It's way quieter than a normal vacuum. You can have a conversation with it running in the same room & not have to raise your voice at all. It’s only slightly annoying to have it running when you’re trying to listen to music/ the TV, or make a phone call.
It fits under all the furniture I have & gets between legs of chairs without me having to lift things, move things out of the way, wrestle with a power cord, then put everything back (the reasons none of us want to have to vacuum).
The dustbin will hold a lot of dirt & cat hair before it needs emptying. It has never had to quit a cleaning session early because the dustbin is too full.
The cats like to watch it work but they haven’t bothered it/ haven’t ridden on it & it hasn’t bothered them. My one cat likes to stand vigil at his food dish & the vacuum will just clean a one-inch circumference around him without trying to bump him out of the way. (It’s quiet enough that they don’t run in terror.)
Cons:
It’s advertised as working on both 2.4 Ghz & 5 Ghz Wi-Fi, but that turns out to be a total lie when you try to set it up &, suddenly, it NEEDS to connect it to the 2.4 Ghz (which I don’t know how to do & it was the specific reason I bought THIS model instead of hundreds of others). I did try pressing random buttons on my router before returning the device & it HAS been working ever since.
I have a raised threshold one half-inch high & four inches wide between two rooms that it continually struggles to climb over. It usually spends about 5 minutes there, trying, before backing down the way it came. Maybe one time in ten it actually makes it into & cleans the other room. - You’re not supposed to pick it up & help it get there, even if you feel sorry for it.
If you have the mop attached it has no chance of climbing onto anything. That’s supposedly a “feature” but when it gets into an area between two carpets and you watch it scoot back & forth repeatedly like a sad lost animal …you kind of feel bad for it.
The “mop” is just a gravity fed water reservoir with a removable (washable) cloth attached to the bottom. It doesn’t actually “mop” anything, so much as give it a very gentle slightly damp dusting. It wouldn’t clean a single dirty footprint off of a hard floor if you ran it for 100 cycles. It would only spread a spill around if it came across one.
The mop function, honestly, is pretty useless unless you have dark hardwood floors that show dust everyday.
When it’s finished cleaning, it goes back to its charging station, which could be a problem if the charging station is kept on a wood floor or carpet with the mop reservoir full (& continuously damp). So, if you’re using the mop, you have to remember to take that attachment off soon after it’s finished cleaning (or damage your floor).
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Reviewed in the United States on August 4, 2025
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